Documentation Verification Report

Operations

📁 Source: Mathlib/RingTheory/Ideal/Quotient/Operations.lean

Statistics

MetricCount
DefinitionsquotientBot, liftOfSurjective, liftSupQuotQuotMk, liftSupQuotQuotMkₐ, quotLeftToQuotSup, quotLeftToQuotSupₐ, quotQuotEquivComm, quotQuotEquivCommₐ, quotQuotEquivQuotOfLE, quotQuotEquivQuotOfLEₐ, quotQuotEquivQuotSup, quotQuotEquivQuotSupₐ, quotQuotMk, quotQuotMkₐ, quotQuotToQuotSup, quotQuotToQuotSupₐ, algebra, algebraQuotientOfLEComap, factorₐ, liftₐ, mkₐ, instAlgebraQuotient, instAlgebraQuotientComapRingHomAlgebraMap, kerLiftAlg, powQuotPowSuccEquivMapMkPowSuccPow, powQuotPowSuccLinearEquivMapMkPowSuccPow, quotientAlgebra, quotientEquiv, quotientEquivAlg, quotientEquivAlgOfEq, quotientInfEquivQuotientProd, quotientInfRingEquivPiQuotient, quotientInfToPiQuotient, quotientKerAlgEquivOfRightInverse, quotientKerAlgEquivOfSurjective, quotientKerEquivRange, quotientMap, quotientMapₐ, quotientMulEquivQuotientProd, quotientBot, kerLift, quotientKerEquivOfRightInverse, quotientKerEquivOfSurjective, quotientKerEquivRange, quotientKerEquivRangeS
45
TheoremsquotientBot_mk, quotientBot_symm_mk, liftOfSurjective_apply, liftOfSurjective_comp, liftOfSurjective_surjective, coe_liftSupQuotQuotMkₐ, coe_quotLeftToQuotSupₐ, coe_quotQuotEquivCommₐ, coe_quotQuotEquivQuotOfLEₐ, coe_quotQuotEquivQuotOfLEₐ_symm, coe_quotQuotEquivQuotSupₐ, coe_quotQuotEquivQuotSupₐ_symm, coe_quotQuotMkₐ, coe_quotQuotToQuotSupₐ, ker_quotLeftToQuotSup, ker_quotQuotMk, liftSupQuotQuotMkₐ_toRingHom, quotLeftToQuotSupₐ_toRingHom, quotQuotEquivComm_algebraMap, quotQuotEquivComm_comp_quotQuotMk, quotQuotEquivComm_comp_quotQuotMkₐ, quotQuotEquivComm_mk_mk, quotQuotEquivComm_quotQuotMk, quotQuotEquivComm_symm, quotQuotEquivComm_symmₐ, quotQuotEquivCommₐ_toRingEquiv, quotQuotEquivQuotOfLE_comp_quotQuotMk, quotQuotEquivQuotOfLE_comp_quotQuotMkₐ, quotQuotEquivQuotOfLE_quotQuotMk, quotQuotEquivQuotOfLE_symm_comp_mk, quotQuotEquivQuotOfLE_symm_comp_mkₐ, quotQuotEquivQuotOfLE_symm_mk, quotQuotEquivQuotOfLEₐ_comp_mkₐ, quotQuotEquivQuotOfLEₐ_symm_toRingEquiv, quotQuotEquivQuotOfLEₐ_toRingEquiv, quotQuotEquivQuotSup_quotQuotMk, quotQuotEquivQuotSup_quot_quot_algebraMap, quotQuotEquivQuotSup_symm_quotQuotMk, quotQuotEquivQuotSupₐ_symm_toRingEquiv, quotQuotEquivQuotSupₐ_toRingEquiv, quotQuotMkₐ_toRingHom, quotQuotToQuotSupₐ_toRingHom, map_smul, algHom_ext, alg_map_eq, algebraMap_eq, coe_factorₐ, factorₐ_apply, factorₐ_apply_mk, factorₐ_comp, factorₐ_comp_mk, factorₐ_refl, isScalarTower, liftₐ_apply, liftₐ_comp, mk_algebraMap, mk_bijective_iff_eq_bot, mk_comp_algebraMap, mkₐ_eq_mk, mkₐ_ker, mkₐ_surjective, mkₐ_toRingHom, smul_top, span_singleton_one, algebraMap_quotient_injective, bot_quotient_isMaximal_iff, comap_map_mk, comap_map_quotientMk, comp_quotientMap_eq_of_comp_eq, exists_forall_sub_mem_ideal, fst_comp_quotientInfEquivQuotientProd, fst_comp_quotientMulEquivQuotientProd, injective_lift_iff, isPrime_map_quotientMk_of_isPrime, kerLiftAlg_injective, kerLiftAlg_mk, kerLiftAlg_toRingHom, ker_Pi_Quotient_mk, ker_quotientMap_mk, ker_quotient_lift, map_mk_eq_bot_of_le, map_quotient_self, mem_quotient_iff_mem, mem_quotient_iff_mem_sup, mk_ker, pi_mkQ_surjective, pi_quotient_surjective, quotientEquivAlgOfEq_coe_eq_factor, quotientEquivAlgOfEq_coe_eq_factorₐ, quotientEquivAlgOfEq_mk, quotientEquivAlgOfEq_symm, quotientEquivAlg_mk, quotientEquivAlg_symm, quotientEquiv_apply, quotientEquiv_mk, quotientEquiv_symm_apply, quotientEquiv_symm_mk, quotientInfEquivQuotientProd_fst, quotientInfEquivQuotientProd_snd, quotientInfToPiQuotient_inj, quotientInfToPiQuotient_mk, quotientInfToPiQuotient_mk', quotientInfToPiQuotient_surj, quotientKerAlgEquivOfRightInverse_apply, quotientKerAlgEquivOfRightInverse_symm_apply, quotientKerAlgEquivOfSurjective_apply, quotientKerAlgEquivOfSurjective_mk, quotientKerAlgEquivOfSurjective_symm_apply, quotientMap_algebraMap, quotientMap_comp_mk, quotientMap_injective, quotientMap_injective', quotientMap_mk, quotientMap_surjective, quotientMulEquivQuotientProd_fst, quotientMulEquivQuotientProd_snd, quotient_map_comp_mkₐ, quotient_map_mkₐ, snd_comp_quotientInfEquivQuotientProd, snd_comp_quotientMulEquivQuotientProd, quotientBot_mk, quotientBot_symm_mk, kerLift_injective, kerLift_mk, lift_injective_of_ker_le_ideal, apply, apply, quotientKerEquivOfSurjective_apply_mk, quotientKerEquivOfSurjective_symm_apply, quotientKerEquivOfSurjective_symm_comp
130
Total175

AlgEquiv

Definitions

NameCategoryTheorems
quotientBot 📖CompOp
2 mathmath: quotientBot_mk, quotientBot_symm_mk

Theorems

NameKindAssumesProvesValidatesDepends On
quotientBot_mk 📖mathematicalDFunLike.coe
AlgEquiv
HasQuotient.Quotient
Ideal
Ring.toSemiring
CommRing.toRing
Ideal.instHasQuotient
Bot.bot
Submodule.instBot
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Ideal.Quotient.ring
Ideal.instIsTwoSidedBot
Ideal.Quotient.algebra
instFunLike
quotientBot
RingHom
Ideal.instIsTwoSided_1
RingHom.instFunLike
Ideal.instIsTwoSidedBot
Ideal.instIsTwoSided_1
quotientBot_symm_mk 📖mathematicalDFunLike.coe
AlgEquiv
HasQuotient.Quotient
Ideal
Ring.toSemiring
CommRing.toRing
Ideal.instHasQuotient
Bot.bot
Submodule.instBot
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Ideal.Quotient.ring
Ideal.instIsTwoSidedBot
Ideal.Quotient.algebra
instFunLike
symm
quotientBot
RingHom
Ideal.instIsTwoSided_1
RingHom.instFunLike
Ideal.instIsTwoSidedBot

AlgHom

Definitions

NameCategoryTheorems
liftOfSurjective 📖CompOp
3 mathmath: liftOfSurjective_surjective, liftOfSurjective_apply, liftOfSurjective_comp

Theorems

NameKindAssumesProvesValidatesDepends On
liftOfSurjective_apply 📖mathematicalDFunLike.coe
AlgHom
CommRing.toCommSemiring
CommSemiring.toSemiring
funLike
Ideal
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
RingHom.ker
RingHom
RingHom.instFunLike
RingHom.instRingHomClass
toRingHom
liftOfSurjectiveRingHom.instRingHomClass
AlgHomClass.toRingHomClass
algHomClass
AlgEquivClass.toAlgHomClass
AlgEquiv.instAlgEquivClass
AlgEquiv.coe_algHom
RingHom.instIsTwoSidedKer
Ideal.quotientKerAlgEquivOfSurjective_symm_apply
liftOfSurjective_comp 📖mathematicalDFunLike.coe
AlgHom
CommRing.toCommSemiring
CommSemiring.toSemiring
funLike
Ideal
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
RingHom.ker
RingHom
RingHom.instFunLike
RingHom.instRingHomClass
toRingHom
comp
liftOfSurjective
RingHom.instRingHomClass
ext
liftOfSurjective_apply
liftOfSurjective_surjective 📖mathematicalDFunLike.coe
AlgHom
CommRing.toCommSemiring
CommSemiring.toSemiring
funLike
Ideal
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
RingHom.ker
RingHom
RingHom.instFunLike
RingHom.instRingHomClass
toRingHom
liftOfSurjectiveRingHom.instRingHomClass
Function.Surjective.of_comp
liftOfSurjective_apply

DoubleQuot

Definitions

NameCategoryTheorems
liftSupQuotQuotMk 📖CompOp
2 mathmath: liftSupQuotQuotMkₐ_toRingHom, coe_liftSupQuotQuotMkₐ
liftSupQuotQuotMkₐ 📖CompOp
2 mathmath: liftSupQuotQuotMkₐ_toRingHom, coe_liftSupQuotQuotMkₐ
quotLeftToQuotSup 📖CompOp
3 mathmath: coe_quotLeftToQuotSupₐ, ker_quotLeftToQuotSup, quotLeftToQuotSupₐ_toRingHom
quotLeftToQuotSupₐ 📖CompOp
2 mathmath: coe_quotLeftToQuotSupₐ, quotLeftToQuotSupₐ_toRingHom
quotQuotEquivComm 📖CompOp
7 mathmath: quotQuotEquivComm_comp_quotQuotMk, quotQuotEquivComm_quotQuotMk, quotQuotEquivCommₐ_toRingEquiv, quotQuotEquivComm_mk_mk, coe_quotQuotEquivCommₐ, quotQuotEquivComm_symm, quotQuotEquivComm_algebraMap
quotQuotEquivCommₐ 📖CompOp
4 mathmath: quotQuotEquivComm_symmₐ, quotQuotEquivCommₐ_toRingEquiv, quotQuotEquivComm_comp_quotQuotMkₐ, coe_quotQuotEquivCommₐ
quotQuotEquivQuotOfLE 📖CompOp
8 mathmath: coe_quotQuotEquivQuotOfLEₐ_symm, quotQuotEquivQuotOfLEₐ_symm_toRingEquiv, coe_quotQuotEquivQuotOfLEₐ, quotQuotEquivQuotOfLEₐ_toRingEquiv, quotQuotEquivQuotOfLE_symm_comp_mk, quotQuotEquivQuotOfLE_symm_mk, quotQuotEquivQuotOfLE_comp_quotQuotMk, quotQuotEquivQuotOfLE_quotQuotMk
quotQuotEquivQuotOfLEₐ 📖CompOp
7 mathmath: coe_quotQuotEquivQuotOfLEₐ_symm, quotQuotEquivQuotOfLEₐ_symm_toRingEquiv, quotQuotEquivQuotOfLE_comp_quotQuotMkₐ, quotQuotEquivQuotOfLE_symm_comp_mkₐ, coe_quotQuotEquivQuotOfLEₐ, quotQuotEquivQuotOfLEₐ_comp_mkₐ, quotQuotEquivQuotOfLEₐ_toRingEquiv
quotQuotEquivQuotSup 📖CompOp
7 mathmath: coe_quotQuotEquivQuotSupₐ, coe_quotQuotEquivQuotSupₐ_symm, quotQuotEquivQuotSup_quotQuotMk, quotQuotEquivQuotSupₐ_toRingEquiv, quotQuotEquivQuotSup_symm_quotQuotMk, quotQuotEquivQuotSup_quot_quot_algebraMap, quotQuotEquivQuotSupₐ_symm_toRingEquiv
quotQuotEquivQuotSupₐ 📖CompOp
4 mathmath: coe_quotQuotEquivQuotSupₐ, coe_quotQuotEquivQuotSupₐ_symm, quotQuotEquivQuotSupₐ_toRingEquiv, quotQuotEquivQuotSupₐ_symm_toRingEquiv
quotQuotMk 📖CompOp
13 mathmath: coe_quotQuotMkₐ, quotQuotEquivComm_comp_quotQuotMk, quotQuotEquivComm_quotQuotMk, AdjoinRoot.quotMapCMapSpanMkEquivQuotMapCQuotMapSpanMk_symm_quotQuotMk, ker_quotQuotMk, quotQuotMkₐ_toRingHom, quotQuotEquivQuotSup_quotQuotMk, AdjoinRoot.quotMapCMapSpanMkEquivQuotMapCQuotMapSpanMk_mk, quotQuotEquivQuotOfLE_symm_comp_mk, quotQuotEquivQuotSup_symm_quotQuotMk, quotQuotEquivQuotOfLE_symm_mk, quotQuotEquivQuotOfLE_comp_quotQuotMk, quotQuotEquivQuotOfLE_quotQuotMk
quotQuotMkₐ 📖CompOp
5 mathmath: coe_quotQuotMkₐ, quotQuotEquivQuotOfLE_comp_quotQuotMkₐ, quotQuotMkₐ_toRingHom, quotQuotEquivQuotOfLE_symm_comp_mkₐ, quotQuotEquivComm_comp_quotQuotMkₐ
quotQuotToQuotSup 📖CompOp
2 mathmath: quotQuotToQuotSupₐ_toRingHom, coe_quotQuotToQuotSupₐ
quotQuotToQuotSupₐ 📖CompOp
2 mathmath: quotQuotToQuotSupₐ_toRingHom, coe_quotQuotToQuotSupₐ

Theorems

NameKindAssumesProvesValidatesDepends On
coe_liftSupQuotQuotMkₐ 📖mathematicalDFunLike.coe
AlgHom
HasQuotient.Quotient
Ideal
CommSemiring.toSemiring
CommRing.toCommSemiring
Ideal.instHasQuotient_1
SemilatticeSup.toMax
IdemSemiring.toSemilatticeSup
Submodule.idemSemiring
Algebra.id
Ring.toSemiring
CommRing.toRing
Ideal.instHasQuotient
Ideal.Quotient.semiring
Ideal.Quotient.commRing
Ideal.map
Ideal.Quotient.ring
Ideal.instIsTwoSided_1
Ideal.Quotient.algebra
AlgHom.funLike
Ideal.Quotient.mkₐ
Ideal.instAlgebraQuotient
liftSupQuotQuotMkₐ
RingHom
Semiring.toNonAssocSemiring
RingHom.instFunLike
liftSupQuotQuotMk
Ideal.instIsTwoSided_1
coe_quotLeftToQuotSupₐ 📖mathematicalDFunLike.coe
AlgHom
HasQuotient.Quotient
Ideal
CommSemiring.toSemiring
CommRing.toCommSemiring
Ideal.instHasQuotient_1
SemilatticeSup.toMax
IdemSemiring.toSemilatticeSup
Submodule.idemSemiring
Algebra.id
Ideal.Quotient.semiring
Ideal.instAlgebraQuotient
AlgHom.funLike
quotLeftToQuotSupₐ
RingHom
Semiring.toNonAssocSemiring
RingHom.instFunLike
quotLeftToQuotSup
coe_quotQuotEquivCommₐ 📖mathematicalDFunLike.coe
AlgEquiv
HasQuotient.Quotient
Ideal
CommSemiring.toSemiring
CommRing.toCommSemiring
Ideal.instHasQuotient_1
Ring.toSemiring
CommRing.toRing
Ideal.instHasQuotient
Ideal.Quotient.semiring
Ideal.Quotient.commRing
Ideal.map
AlgHom
Ideal.Quotient.ring
Ideal.instIsTwoSided_1
Ideal.Quotient.algebra
AlgHom.funLike
Ideal.Quotient.mkₐ
Ideal.instAlgebraQuotient
AlgEquiv.instFunLike
quotQuotEquivCommₐ
RingEquiv
RingHom
Semiring.toNonAssocSemiring
RingHom.instFunLike
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Distrib.toAdd
EquivLike.toFunLike
RingEquiv.instEquivLike
quotQuotEquivComm
Ideal.instIsTwoSided_1
coe_quotQuotEquivQuotOfLEₐ 📖mathematicalIdeal
CommSemiring.toSemiring
CommRing.toCommSemiring
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
DFunLike.coe
AlgEquiv
HasQuotient.Quotient
Ideal.instHasQuotient_1
Ring.toSemiring
CommRing.toRing
Ideal.instHasQuotient
Ideal.Quotient.semiring
Ideal.Quotient.commRing
Ideal.map
AlgHom
Ideal.Quotient.ring
Ideal.instIsTwoSided_1
Ideal.Quotient.algebra
AlgHom.funLike
Ideal.Quotient.mkₐ
Ideal.instAlgebraQuotient
AlgEquiv.instFunLike
quotQuotEquivQuotOfLEₐ
RingEquiv
RingHom
RingHom.instFunLike
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Distrib.toAdd
EquivLike.toFunLike
RingEquiv.instEquivLike
quotQuotEquivQuotOfLE
Ideal.instIsTwoSided_1
coe_quotQuotEquivQuotOfLEₐ_symm 📖mathematicalIdeal
CommSemiring.toSemiring
CommRing.toCommSemiring
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
DFunLike.coe
AlgEquiv
HasQuotient.Quotient
Ideal.instHasQuotient_1
Ring.toSemiring
CommRing.toRing
Ideal.instHasQuotient
Ideal.Quotient.semiring
Ideal.Quotient.commRing
Ideal.map
AlgHom
Ideal.Quotient.ring
Ideal.instIsTwoSided_1
Ideal.Quotient.algebra
AlgHom.funLike
Ideal.Quotient.mkₐ
Ideal.instAlgebraQuotient
AlgEquiv.instFunLike
AlgEquiv.symm
quotQuotEquivQuotOfLEₐ
RingEquiv
RingHom
RingHom.instFunLike
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Distrib.toAdd
EquivLike.toFunLike
RingEquiv.instEquivLike
RingEquiv.symm
quotQuotEquivQuotOfLE
Ideal.instIsTwoSided_1
coe_quotQuotEquivQuotSupₐ 📖mathematicalDFunLike.coe
AlgEquiv
HasQuotient.Quotient
Ideal
CommSemiring.toSemiring
CommRing.toCommSemiring
Ideal.instHasQuotient_1
Ring.toSemiring
CommRing.toRing
Ideal.instHasQuotient
Ideal.Quotient.semiring
Ideal.Quotient.commRing
Ideal.map
AlgHom
Ideal.Quotient.ring
Ideal.instIsTwoSided_1
Ideal.Quotient.algebra
AlgHom.funLike
Ideal.Quotient.mkₐ
SemilatticeSup.toMax
IdemSemiring.toSemilatticeSup
Submodule.idemSemiring
Algebra.id
Ideal.instAlgebraQuotient
AlgEquiv.instFunLike
quotQuotEquivQuotSupₐ
RingEquiv
RingHom
Semiring.toNonAssocSemiring
RingHom.instFunLike
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Distrib.toAdd
EquivLike.toFunLike
RingEquiv.instEquivLike
quotQuotEquivQuotSup
Ideal.instIsTwoSided_1
coe_quotQuotEquivQuotSupₐ_symm 📖mathematicalDFunLike.coe
AlgEquiv
HasQuotient.Quotient
Ideal
CommSemiring.toSemiring
CommRing.toCommSemiring
Ideal.instHasQuotient_1
SemilatticeSup.toMax
IdemSemiring.toSemilatticeSup
Submodule.idemSemiring
Algebra.id
Ring.toSemiring
CommRing.toRing
Ideal.instHasQuotient
Ideal.Quotient.semiring
Ideal.Quotient.commRing
Ideal.map
AlgHom
Ideal.Quotient.ring
Ideal.instIsTwoSided_1
Ideal.Quotient.algebra
AlgHom.funLike
Ideal.Quotient.mkₐ
Ideal.instAlgebraQuotient
AlgEquiv.instFunLike
AlgEquiv.symm
quotQuotEquivQuotSupₐ
RingEquiv
RingHom
Semiring.toNonAssocSemiring
RingHom.instFunLike
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Distrib.toAdd
EquivLike.toFunLike
RingEquiv.instEquivLike
RingEquiv.symm
quotQuotEquivQuotSup
Ideal.instIsTwoSided_1
coe_quotQuotMkₐ 📖mathematicalDFunLike.coe
AlgHom
HasQuotient.Quotient
Ideal
CommSemiring.toSemiring
CommRing.toCommSemiring
Ideal.instHasQuotient_1
Ring.toSemiring
CommRing.toRing
Ideal.instHasQuotient
Ideal.Quotient.semiring
Ideal.Quotient.commRing
Ideal.map
Ideal.Quotient.ring
Ideal.instIsTwoSided_1
Ideal.Quotient.algebra
AlgHom.funLike
Ideal.Quotient.mkₐ
Ideal.instAlgebraQuotient
quotQuotMkₐ
RingHom
Semiring.toNonAssocSemiring
RingHom.instFunLike
quotQuotMk
Ideal.instIsTwoSided_1
coe_quotQuotToQuotSupₐ 📖mathematicalDFunLike.coe
AlgHom
HasQuotient.Quotient
Ideal
CommSemiring.toSemiring
CommRing.toCommSemiring
Ideal.instHasQuotient_1
Ring.toSemiring
CommRing.toRing
Ideal.instHasQuotient
Ideal.Quotient.semiring
Ideal.Quotient.commRing
Ideal.map
Ideal.Quotient.ring
Ideal.instIsTwoSided_1
Ideal.Quotient.algebra
AlgHom.funLike
Ideal.Quotient.mkₐ
SemilatticeSup.toMax
IdemSemiring.toSemilatticeSup
Submodule.idemSemiring
Algebra.id
Ideal.instAlgebraQuotient
quotQuotToQuotSupₐ
RingHom
Semiring.toNonAssocSemiring
RingHom.instFunLike
quotQuotToQuotSup
Ideal.instIsTwoSided_1
ker_quotLeftToQuotSup 📖mathematicalRingHom.ker
HasQuotient.Quotient
Ideal
CommSemiring.toSemiring
CommRing.toCommSemiring
Ideal.instHasQuotient_1
SemilatticeSup.toMax
IdemSemiring.toSemilatticeSup
Submodule.idemSemiring
Algebra.id
RingHom
Semiring.toNonAssocSemiring
Ideal.Quotient.semiring
RingHom.instFunLike
RingHom.instRingHomClass
quotLeftToQuotSup
Ideal.map
Ring.toSemiring
CommRing.toRing
Ideal.instHasQuotient
Ideal.Quotient.ring
Ideal.instIsTwoSided_1
RingHom.instRingHomClass
Ideal.instIsTwoSided_1
Ideal.ker_quotient_lift
Ideal.mk_ker
Ideal.map_eq_iff_sup_ker_eq_of_surjective
Quotient.mk_surjective
sup_comm
sup_idem
ker_quotQuotMk 📖mathematicalRingHom.ker
HasQuotient.Quotient
Ideal
CommSemiring.toSemiring
CommRing.toCommSemiring
Ideal.instHasQuotient_1
Ring.toSemiring
CommRing.toRing
Ideal.instHasQuotient
Ideal.Quotient.semiring
Ideal.Quotient.commRing
Ideal.map
RingHom
Semiring.toNonAssocSemiring
Ideal.Quotient.ring
Ideal.instIsTwoSided_1
RingHom.instFunLike
RingHom.instRingHomClass
quotQuotMk
SemilatticeSup.toMax
IdemSemiring.toSemilatticeSup
Submodule.idemSemiring
Algebra.id
Ideal.instIsTwoSided_1
RingHom.instRingHomClass
RingHom.ker_eq_comap_bot
quotQuotMk.eq_1
Ideal.comap_comap
RingHom.ker.eq_1
Ideal.mk_ker
Ideal.comap_map_of_surjective
Ideal.Quotient.mk_surjective
sup_comm
liftSupQuotQuotMkₐ_toRingHom 📖mathematicalRingHomClass.toRingHom
AlgHom
HasQuotient.Quotient
Ideal
CommSemiring.toSemiring
CommRing.toCommSemiring
Ideal.instHasQuotient_1
SemilatticeSup.toMax
IdemSemiring.toSemilatticeSup
Submodule.idemSemiring
Algebra.id
Ring.toSemiring
CommRing.toRing
Ideal.instHasQuotient
Ideal.Quotient.semiring
Ideal.Quotient.commRing
Ideal.map
Ideal.Quotient.ring
Ideal.instIsTwoSided_1
Ideal.Quotient.algebra
AlgHom.funLike
Ideal.Quotient.mkₐ
Ideal.instAlgebraQuotient
Semiring.toNonAssocSemiring
AlgHomClass.toRingHomClass
AlgHom.algHomClass
liftSupQuotQuotMkₐ
liftSupQuotQuotMk
Ideal.instIsTwoSided_1
AlgHomClass.toRingHomClass
AlgHom.algHomClass
quotLeftToQuotSupₐ_toRingHom 📖mathematicalRingHomClass.toRingHom
AlgHom
HasQuotient.Quotient
Ideal
CommSemiring.toSemiring
CommRing.toCommSemiring
Ideal.instHasQuotient_1
SemilatticeSup.toMax
IdemSemiring.toSemilatticeSup
Submodule.idemSemiring
Algebra.id
Ideal.Quotient.semiring
Ideal.instAlgebraQuotient
AlgHom.funLike
Semiring.toNonAssocSemiring
AlgHomClass.toRingHomClass
AlgHom.algHomClass
quotLeftToQuotSupₐ
quotLeftToQuotSup
AlgHomClass.toRingHomClass
AlgHom.algHomClass
quotQuotEquivComm_algebraMap 📖mathematicalDFunLike.coe
RingEquiv
HasQuotient.Quotient
Ideal
CommSemiring.toSemiring
CommRing.toCommSemiring
Ideal.instHasQuotient_1
Ring.toSemiring
CommRing.toRing
Ideal.instHasQuotient
Ideal.Quotient.semiring
Ideal.Quotient.commRing
Ideal.map
RingHom
Semiring.toNonAssocSemiring
Ideal.Quotient.ring
Ideal.instIsTwoSided_1
RingHom.instFunLike
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Distrib.toAdd
EquivLike.toFunLike
RingEquiv.instEquivLike
quotQuotEquivComm
algebraMap
Ideal.instAlgebraQuotient
Ideal.instIsTwoSided_1
quotQuotEquivComm_comp_quotQuotMk 📖mathematicalRingHom.comp
HasQuotient.Quotient
Ideal
CommSemiring.toSemiring
CommRing.toCommSemiring
Ideal.instHasQuotient_1
Ring.toSemiring
CommRing.toRing
Ideal.instHasQuotient
Ideal.Quotient.semiring
Ideal.Quotient.commRing
Ideal.map
RingHom
Semiring.toNonAssocSemiring
Ideal.Quotient.ring
Ideal.instIsTwoSided_1
RingHom.instFunLike
RingHomClass.toRingHom
RingEquiv
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Distrib.toAdd
EquivLike.toFunLike
RingEquiv.instEquivLike
RingEquivClass.toRingHomClass
RingEquiv.instRingEquivClass
quotQuotEquivComm
quotQuotMk
RingHom.ext
Ideal.instIsTwoSided_1
RingEquivClass.toRingHomClass
RingEquiv.instRingEquivClass
quotQuotEquivComm_quotQuotMk
quotQuotEquivComm_comp_quotQuotMkₐ 📖mathematicalAlgHom.comp
HasQuotient.Quotient
Ideal
CommSemiring.toSemiring
CommRing.toCommSemiring
Ideal.instHasQuotient_1
Ring.toSemiring
CommRing.toRing
Ideal.instHasQuotient
Ideal.Quotient.semiring
Ideal.Quotient.commRing
Ideal.map
AlgHom
Ideal.Quotient.ring
Ideal.instIsTwoSided_1
Ideal.Quotient.algebra
AlgHom.funLike
Ideal.Quotient.mkₐ
Ideal.instAlgebraQuotient
AlgHomClass.toAlgHom
AlgEquiv
AlgEquiv.instFunLike
AlgEquivClass.toAlgHomClass
AlgEquiv.instEquivLike
AlgEquiv.instAlgEquivClass
quotQuotEquivCommₐ
quotQuotMkₐ
AlgHom.ext
Ideal.instIsTwoSided_1
AlgEquivClass.toAlgHomClass
AlgEquiv.instAlgEquivClass
quotQuotEquivComm_quotQuotMk
quotQuotEquivComm_mk_mk 📖mathematicalDFunLike.coe
RingEquiv
HasQuotient.Quotient
Ideal
CommSemiring.toSemiring
CommRing.toCommSemiring
Ideal.instHasQuotient_1
Ring.toSemiring
CommRing.toRing
Ideal.instHasQuotient
Ideal.Quotient.semiring
Ideal.Quotient.commRing
Ideal.map
RingHom
Semiring.toNonAssocSemiring
Ideal.Quotient.ring
Ideal.instIsTwoSided_1
RingHom.instFunLike
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Distrib.toAdd
EquivLike.toFunLike
RingEquiv.instEquivLike
quotQuotEquivComm
Ideal.Quotient.instRingQuotient
algebraMap
Ideal.instAlgebraQuotient
Algebra.id
Ideal.instIsTwoSided_1
quotQuotEquivComm_quotQuotMk 📖mathematicalDFunLike.coe
RingEquiv
HasQuotient.Quotient
Ideal
CommSemiring.toSemiring
CommRing.toCommSemiring
Ideal.instHasQuotient_1
Ring.toSemiring
CommRing.toRing
Ideal.instHasQuotient
Ideal.Quotient.semiring
Ideal.Quotient.commRing
Ideal.map
RingHom
Semiring.toNonAssocSemiring
Ideal.Quotient.ring
Ideal.instIsTwoSided_1
RingHom.instFunLike
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Distrib.toAdd
EquivLike.toFunLike
RingEquiv.instEquivLike
quotQuotEquivComm
quotQuotMk
Ideal.instIsTwoSided_1
quotQuotEquivComm_symm 📖mathematicalRingEquiv.symm
HasQuotient.Quotient
Ideal
CommSemiring.toSemiring
CommRing.toCommSemiring
Ideal.instHasQuotient_1
Ring.toSemiring
CommRing.toRing
Ideal.instHasQuotient
Ideal.Quotient.semiring
Ideal.Quotient.commRing
Ideal.map
RingHom
Semiring.toNonAssocSemiring
Ideal.Quotient.ring
Ideal.instIsTwoSided_1
RingHom.instFunLike
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Distrib.toAdd
quotQuotEquivComm
Ideal.instIsTwoSided_1
quotQuotEquivComm_symmₐ 📖mathematicalAlgEquiv.symm
HasQuotient.Quotient
Ideal
CommSemiring.toSemiring
CommRing.toCommSemiring
Ideal.instHasQuotient_1
Ring.toSemiring
CommRing.toRing
Ideal.instHasQuotient
Ideal.Quotient.semiring
Ideal.Quotient.commRing
Ideal.map
AlgHom
Ideal.Quotient.ring
Ideal.instIsTwoSided_1
Ideal.Quotient.algebra
AlgHom.funLike
Ideal.Quotient.mkₐ
Ideal.instAlgebraQuotient
quotQuotEquivCommₐ
Ideal.instIsTwoSided_1
quotQuotEquivCommₐ_toRingEquiv 📖mathematicalRingEquivClass.toRingEquiv
AlgEquiv
HasQuotient.Quotient
Ideal
CommSemiring.toSemiring
CommRing.toCommSemiring
Ideal.instHasQuotient_1
Ring.toSemiring
CommRing.toRing
Ideal.instHasQuotient
Ideal.Quotient.semiring
Ideal.Quotient.commRing
Ideal.map
AlgHom
Ideal.Quotient.ring
Ideal.instIsTwoSided_1
Ideal.Quotient.algebra
AlgHom.funLike
Ideal.Quotient.mkₐ
Ideal.instAlgebraQuotient
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Distrib.toAdd
AlgEquiv.instEquivLike
AlgEquivClass.toRingEquivClass
AlgEquiv.instAlgEquivClass
quotQuotEquivCommₐ
quotQuotEquivComm
Ideal.instIsTwoSided_1
AlgEquivClass.toRingEquivClass
AlgEquiv.instAlgEquivClass
quotQuotEquivQuotOfLE_comp_quotQuotMk 📖mathematicalIdeal
CommSemiring.toSemiring
CommRing.toCommSemiring
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
RingHom.comp
HasQuotient.Quotient
Ideal.instHasQuotient_1
Ring.toSemiring
CommRing.toRing
Ideal.instHasQuotient
Ideal.Quotient.semiring
Ideal.Quotient.commRing
Ideal.map
RingHom
Ideal.Quotient.ring
Ideal.instIsTwoSided_1
RingHom.instFunLike
RingHomClass.toRingHom
RingEquiv
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Distrib.toAdd
EquivLike.toFunLike
RingEquiv.instEquivLike
RingEquivClass.toRingHomClass
RingEquiv.instRingEquivClass
quotQuotEquivQuotOfLE
quotQuotMk
RingHom.ext
Ideal.instIsTwoSided_1
RingEquivClass.toRingHomClass
RingEquiv.instRingEquivClass
quotQuotEquivQuotOfLE_comp_quotQuotMkₐ 📖mathematicalIdeal
CommSemiring.toSemiring
CommRing.toCommSemiring
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
AlgHom.comp
HasQuotient.Quotient
Ideal.instHasQuotient_1
Ring.toSemiring
CommRing.toRing
Ideal.instHasQuotient
Ideal.Quotient.semiring
Ideal.Quotient.commRing
Ideal.map
AlgHom
Ideal.Quotient.ring
Ideal.instIsTwoSided_1
Ideal.Quotient.algebra
AlgHom.funLike
Ideal.Quotient.mkₐ
Ideal.instAlgebraQuotient
AlgHomClass.toAlgHom
AlgEquiv
AlgEquiv.instFunLike
AlgEquivClass.toAlgHomClass
AlgEquiv.instEquivLike
AlgEquiv.instAlgEquivClass
quotQuotEquivQuotOfLEₐ
quotQuotMkₐ
Ideal.instIsTwoSided_1
AlgEquivClass.toAlgHomClass
AlgEquiv.instAlgEquivClass
quotQuotEquivQuotOfLE_quotQuotMk 📖mathematicalIdeal
CommSemiring.toSemiring
CommRing.toCommSemiring
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
DFunLike.coe
RingEquiv
HasQuotient.Quotient
Ideal.instHasQuotient_1
Ring.toSemiring
CommRing.toRing
Ideal.instHasQuotient
Ideal.Quotient.semiring
Ideal.Quotient.commRing
Ideal.map
RingHom
Ideal.Quotient.ring
Ideal.instIsTwoSided_1
RingHom.instFunLike
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Distrib.toAdd
EquivLike.toFunLike
RingEquiv.instEquivLike
quotQuotEquivQuotOfLE
quotQuotMk
Ideal.instIsTwoSided_1
quotQuotEquivQuotOfLE_symm_comp_mk 📖mathematicalIdeal
CommSemiring.toSemiring
CommRing.toCommSemiring
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
RingHom.comp
HasQuotient.Quotient
Ring.toSemiring
CommRing.toRing
Ideal.instHasQuotient
Ideal.instHasQuotient_1
Ideal.Quotient.semiring
Ideal.Quotient.commRing
Ideal.map
RingHom
Ideal.Quotient.ring
Ideal.instIsTwoSided_1
RingHom.instFunLike
RingHomClass.toRingHom
RingEquiv
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Distrib.toAdd
EquivLike.toFunLike
RingEquiv.instEquivLike
RingEquivClass.toRingHomClass
RingEquiv.instRingEquivClass
RingEquiv.symm
quotQuotEquivQuotOfLE
quotQuotMk
RingHom.ext
Ideal.instIsTwoSided_1
RingEquivClass.toRingHomClass
RingEquiv.instRingEquivClass
quotQuotEquivQuotOfLE_symm_comp_mkₐ 📖mathematicalIdeal
CommSemiring.toSemiring
CommRing.toCommSemiring
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
AlgHom.comp
HasQuotient.Quotient
Ring.toSemiring
CommRing.toRing
Ideal.instHasQuotient
Ideal.instHasQuotient_1
Ideal.Quotient.semiring
Ideal.Quotient.commRing
Ideal.map
AlgHom
Ideal.Quotient.ring
Ideal.instIsTwoSided_1
Ideal.Quotient.algebra
AlgHom.funLike
Ideal.Quotient.mkₐ
Ideal.instAlgebraQuotient
AlgHomClass.toAlgHom
AlgEquiv
AlgEquiv.instFunLike
AlgEquivClass.toAlgHomClass
AlgEquiv.instEquivLike
AlgEquiv.instAlgEquivClass
AlgEquiv.symm
quotQuotEquivQuotOfLEₐ
quotQuotMkₐ
Ideal.instIsTwoSided_1
AlgEquivClass.toAlgHomClass
AlgEquiv.instAlgEquivClass
quotQuotEquivQuotOfLE_symm_mk 📖mathematicalIdeal
CommSemiring.toSemiring
CommRing.toCommSemiring
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
DFunLike.coe
RingEquiv
HasQuotient.Quotient
Ideal.instHasQuotient_1
Ring.toSemiring
CommRing.toRing
Ideal.instHasQuotient
Ideal.Quotient.semiring
Ideal.Quotient.commRing
Ideal.map
RingHom
Ideal.Quotient.ring
Ideal.instIsTwoSided_1
RingHom.instFunLike
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Distrib.toAdd
EquivLike.toFunLike
RingEquiv.instEquivLike
RingEquiv.symm
quotQuotEquivQuotOfLE
quotQuotMk
Ideal.instIsTwoSided_1
quotQuotEquivQuotOfLEₐ_comp_mkₐ 📖mathematicalIdeal
CommSemiring.toSemiring
CommRing.toCommSemiring
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
AlgHom.comp
HasQuotient.Quotient
Ideal.instHasQuotient_1
Ring.toSemiring
CommRing.toRing
Ideal.instHasQuotient
Ideal.Quotient.semiring
Ideal.Quotient.commRing
Ideal.map
AlgHom
Ideal.Quotient.ring
Ideal.instIsTwoSided_1
Ideal.Quotient.algebra
AlgHom.funLike
Ideal.Quotient.mkₐ
Ideal.Quotient.instRingQuotient
Ideal.instAlgebraQuotient
AlgEquiv.toAlgHom
quotQuotEquivQuotOfLEₐ
Ideal.Quotient.factorₐ
AlgHom.ext
Ideal.instIsTwoSided_1
Ideal.Quotient.mk_surjective
quotQuotEquivQuotOfLEₐ_symm_toRingEquiv 📖mathematicalIdeal
CommSemiring.toSemiring
CommRing.toCommSemiring
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
RingEquivClass.toRingEquiv
AlgEquiv
HasQuotient.Quotient
Ideal.instHasQuotient_1
Ring.toSemiring
CommRing.toRing
Ideal.instHasQuotient
Ideal.Quotient.semiring
Ideal.Quotient.commRing
Ideal.map
AlgHom
Ideal.Quotient.ring
Ideal.instIsTwoSided_1
Ideal.Quotient.algebra
AlgHom.funLike
Ideal.Quotient.mkₐ
Ideal.instAlgebraQuotient
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Distrib.toAdd
AlgEquiv.instEquivLike
AlgEquivClass.toRingEquivClass
AlgEquiv.instAlgEquivClass
AlgEquiv.symm
quotQuotEquivQuotOfLEₐ
RingEquiv.symm
RingHom
RingHom.instFunLike
quotQuotEquivQuotOfLE
Ideal.instIsTwoSided_1
AlgEquivClass.toRingEquivClass
AlgEquiv.instAlgEquivClass
quotQuotEquivQuotOfLEₐ_toRingEquiv 📖mathematicalIdeal
CommSemiring.toSemiring
CommRing.toCommSemiring
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
RingEquivClass.toRingEquiv
AlgEquiv
HasQuotient.Quotient
Ideal.instHasQuotient_1
Ring.toSemiring
CommRing.toRing
Ideal.instHasQuotient
Ideal.Quotient.semiring
Ideal.Quotient.commRing
Ideal.map
AlgHom
Ideal.Quotient.ring
Ideal.instIsTwoSided_1
Ideal.Quotient.algebra
AlgHom.funLike
Ideal.Quotient.mkₐ
Ideal.instAlgebraQuotient
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Distrib.toAdd
AlgEquiv.instEquivLike
AlgEquivClass.toRingEquivClass
AlgEquiv.instAlgEquivClass
quotQuotEquivQuotOfLEₐ
quotQuotEquivQuotOfLE
Ideal.instIsTwoSided_1
AlgEquivClass.toRingEquivClass
AlgEquiv.instAlgEquivClass
quotQuotEquivQuotSup_quotQuotMk 📖mathematicalDFunLike.coe
RingEquiv
HasQuotient.Quotient
Ideal
CommSemiring.toSemiring
CommRing.toCommSemiring
Ideal.instHasQuotient_1
Ring.toSemiring
CommRing.toRing
Ideal.instHasQuotient
Ideal.Quotient.semiring
Ideal.Quotient.commRing
Ideal.map
RingHom
Semiring.toNonAssocSemiring
Ideal.Quotient.ring
Ideal.instIsTwoSided_1
RingHom.instFunLike
SemilatticeSup.toMax
IdemSemiring.toSemilatticeSup
Submodule.idemSemiring
Algebra.id
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Distrib.toAdd
EquivLike.toFunLike
RingEquiv.instEquivLike
quotQuotEquivQuotSup
quotQuotMk
Ideal.instIsTwoSided_1
quotQuotEquivQuotSup_quot_quot_algebraMap 📖mathematicalDFunLike.coe
RingEquiv
HasQuotient.Quotient
Ideal
CommSemiring.toSemiring
CommRing.toCommSemiring
Ideal.instHasQuotient_1
Ring.toSemiring
CommRing.toRing
Ideal.instHasQuotient
Ideal.Quotient.semiring
Ideal.Quotient.commRing
Ideal.map
RingHom
Semiring.toNonAssocSemiring
Ideal.Quotient.ring
Ideal.instIsTwoSided_1
RingHom.instFunLike
SemilatticeSup.toMax
IdemSemiring.toSemilatticeSup
Submodule.idemSemiring
Algebra.id
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Distrib.toAdd
EquivLike.toFunLike
RingEquiv.instEquivLike
quotQuotEquivQuotSup
algebraMap
Ideal.instAlgebraQuotient
Ideal.instIsTwoSided_1
quotQuotEquivQuotSup_symm_quotQuotMk 📖mathematicalDFunLike.coe
RingEquiv
HasQuotient.Quotient
Ideal
CommSemiring.toSemiring
CommRing.toCommSemiring
Ideal.instHasQuotient_1
SemilatticeSup.toMax
IdemSemiring.toSemilatticeSup
Submodule.idemSemiring
Algebra.id
Ring.toSemiring
CommRing.toRing
Ideal.instHasQuotient
Ideal.Quotient.semiring
Ideal.Quotient.commRing
Ideal.map
RingHom
Semiring.toNonAssocSemiring
Ideal.Quotient.ring
Ideal.instIsTwoSided_1
RingHom.instFunLike
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Distrib.toAdd
EquivLike.toFunLike
RingEquiv.instEquivLike
RingEquiv.symm
quotQuotEquivQuotSup
quotQuotMk
Ideal.instIsTwoSided_1
quotQuotEquivQuotSupₐ_symm_toRingEquiv 📖mathematicalRingEquivClass.toRingEquiv
AlgEquiv
HasQuotient.Quotient
Ideal
CommSemiring.toSemiring
CommRing.toCommSemiring
Ideal.instHasQuotient_1
SemilatticeSup.toMax
IdemSemiring.toSemilatticeSup
Submodule.idemSemiring
Algebra.id
Ring.toSemiring
CommRing.toRing
Ideal.instHasQuotient
Ideal.Quotient.semiring
Ideal.Quotient.commRing
Ideal.map
AlgHom
Ideal.Quotient.ring
Ideal.instIsTwoSided_1
Ideal.Quotient.algebra
AlgHom.funLike
Ideal.Quotient.mkₐ
Ideal.instAlgebraQuotient
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Distrib.toAdd
AlgEquiv.instEquivLike
AlgEquivClass.toRingEquivClass
AlgEquiv.instAlgEquivClass
AlgEquiv.symm
quotQuotEquivQuotSupₐ
RingEquiv.symm
RingHom
Semiring.toNonAssocSemiring
RingHom.instFunLike
quotQuotEquivQuotSup
Ideal.instIsTwoSided_1
AlgEquivClass.toRingEquivClass
AlgEquiv.instAlgEquivClass
quotQuotEquivQuotSupₐ_toRingEquiv 📖mathematicalRingEquivClass.toRingEquiv
AlgEquiv
HasQuotient.Quotient
Ideal
CommSemiring.toSemiring
CommRing.toCommSemiring
Ideal.instHasQuotient_1
Ring.toSemiring
CommRing.toRing
Ideal.instHasQuotient
Ideal.Quotient.semiring
Ideal.Quotient.commRing
Ideal.map
AlgHom
Ideal.Quotient.ring
Ideal.instIsTwoSided_1
Ideal.Quotient.algebra
AlgHom.funLike
Ideal.Quotient.mkₐ
SemilatticeSup.toMax
IdemSemiring.toSemilatticeSup
Submodule.idemSemiring
Algebra.id
Ideal.instAlgebraQuotient
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Distrib.toAdd
AlgEquiv.instEquivLike
AlgEquivClass.toRingEquivClass
AlgEquiv.instAlgEquivClass
quotQuotEquivQuotSupₐ
quotQuotEquivQuotSup
Ideal.instIsTwoSided_1
AlgEquivClass.toRingEquivClass
AlgEquiv.instAlgEquivClass
quotQuotMkₐ_toRingHom 📖mathematicalRingHomClass.toRingHom
AlgHom
HasQuotient.Quotient
Ideal
CommSemiring.toSemiring
CommRing.toCommSemiring
Ideal.instHasQuotient_1
Ring.toSemiring
CommRing.toRing
Ideal.instHasQuotient
Ideal.Quotient.semiring
Ideal.Quotient.commRing
Ideal.map
Ideal.Quotient.ring
Ideal.instIsTwoSided_1
Ideal.Quotient.algebra
AlgHom.funLike
Ideal.Quotient.mkₐ
Ideal.instAlgebraQuotient
Semiring.toNonAssocSemiring
AlgHomClass.toRingHomClass
AlgHom.algHomClass
quotQuotMkₐ
quotQuotMk
Ideal.instIsTwoSided_1
AlgHomClass.toRingHomClass
AlgHom.algHomClass
quotQuotToQuotSupₐ_toRingHom 📖mathematicalRingHomClass.toRingHom
AlgHom
HasQuotient.Quotient
Ideal
CommSemiring.toSemiring
CommRing.toCommSemiring
Ideal.instHasQuotient_1
Ring.toSemiring
CommRing.toRing
Ideal.instHasQuotient
Ideal.Quotient.semiring
Ideal.Quotient.commRing
Ideal.map
Ideal.Quotient.ring
Ideal.instIsTwoSided_1
Ideal.Quotient.algebra
AlgHom.funLike
Ideal.Quotient.mkₐ
SemilatticeSup.toMax
IdemSemiring.toSemilatticeSup
Submodule.idemSemiring
Algebra.id
Ideal.instAlgebraQuotient
Semiring.toNonAssocSemiring
AlgHomClass.toRingHomClass
AlgHom.algHomClass
quotQuotToQuotSupₐ
quotQuotToQuotSup
Ideal.instIsTwoSided_1
AlgHomClass.toRingHomClass
AlgHom.algHomClass

Ideal

Definitions

NameCategoryTheorems
instAlgebraQuotient 📖CompOp
130 mathmath: PowerSeries.IsWeierstrassFactorizationAt.algEquivQuotient_apply, PowerSeries.IsWeierstrassFactorizationAt.algEquivQuotient_symm_apply, Algebra.PreSubmersivePresentation.jacobiMatrix_naive, Algebra.FiniteType.quotient, DoubleQuot.liftSupQuotQuotMkₐ_toRingHom, Algebra.Presentation.naive_toGenerators, Algebra.PreSubmersivePresentation.ofHasCoeffs_map, DoubleQuot.coe_quotQuotEquivQuotOfLEₐ_symm, Polynomial.fiberEquivQuotient_tmul, Polynomial.quotientSpanXSubCAlgEquiv_symm_apply, DoubleQuot.coe_quotQuotMkₐ, StandardEtalePresentation.toPresentation_algebra_smul, PowerBasis.quotientEquivQuotientMinpolyMap_apply, DoubleQuot.coe_quotLeftToQuotSupₐ, AdicCompletion.val_smul_eq_evalₐ_smul, range_cotangentToQuotientSquare, Algebra.QuasiFinite.instQuotientIdeal, AlgEquiv.prodQuotientOfIsIdempotentElem_apply, DoubleQuot.quotQuotEquivQuotOfLEₐ_symm_toRingEquiv, Algebra.Generators.compLocalizationAwayAlgHom_toAlgHom_toComp, DoubleQuot.quotQuotEquivComm_symmₐ, Algebra.PreSubmersivePresentation.ofHasCoeffs_relation, AdjoinRoot.quotEquivQuotMap_symm_apply_mk, Quotient.algebraMap_eq, Algebra.PreSubmersivePresentation.ofHasCoeffs_σ', Algebra.Presentation.quotientEquiv_symm, AdicCompletion.factor_eval_eq_evalₐ, Algebra.Generators.naive_val, PowerBasis.quotientEquivQuotientMinpolyMap_apply_mk, DoubleQuot.quotQuotToQuotSupₐ_toRingHom, Algebra.Generators.compLocalizationAwayAlgHom_X_inl, Algebra.Presentation.naive_relation, IsLocalization.AtPrime.exists_algebraMap_quot_eq_of_mem_quot, StandardEtalePair.equivMvPolynomialQuotient_symm_apply, PowerBasis.quotientEquivQuotientMinpolyMap_symm_apply_mk, KaehlerDifferential.End_equiv_aux, Algebra.PreSubmersivePresentation.ofHasCoeffs_algebra_algebraMap_apply, liftOfDerivationToSquareZero_mk_apply, isStronglyTranscendental_mk_radical_conductor, IsLocalization.Away.mvPolynomialQuotientEquiv_apply, Algebra.Presentation.naive_relation_apply, AdjoinRoot.quotEquivQuotMap_apply, Algebra.Generators.sq_ker_comp_le_ker_compLocalizationAwayAlgHom, DoubleQuot.quotQuotEquivQuotOfLE_comp_quotQuotMkₐ, Algebra.FormallySmooth.mk_lift, AdicCompletion.factorₐ_evalₐ_one, Algebra.PreSubmersivePresentation.naive_toPresentation, Polynomial.quotientSpanXSubCAlgEquiv_mk, AdicCompletion.mk_ofAlgEquiv_symm, DoubleQuot.coe_quotQuotEquivQuotSupₐ, tensorKaehlerQuotKerSqEquiv_symm_tmul_D, Quotient.alg_map_eq, exists_integral_inj_algHom_of_quotient, IsLocalization.Away.quotient_of_isIdempotentElem, DoubleQuot.coe_quotQuotEquivQuotSupₐ_symm, tensorKaehlerQuotKerSqEquiv_tmul_D, derivationToSquareZeroEquivLift_symm_apply_apply_coe, DoubleQuot.quotQuotMkₐ_toRingHom, DoubleQuot.quotQuotEquivQuotOfLE_symm_comp_mkₐ, AdjoinRoot.quotEquivQuotMap_apply_mk, PowerBasis.quotientEquivQuotientMinpolyMap_symm_apply, Algebra.Presentation.tensorModelOfHasCoeffsEquiv_tmul, Algebra.Presentation.tensorModelOfHasCoeffsHom_tmul, IsAdicComplete.mk_liftAlgHom, cotangentEquivIdeal_apply, DoubleQuot.coe_quotQuotEquivQuotOfLEₐ, AdicCompletion.evalOneₐ_of, Algebra.FormallySmooth.iff_split_surjection, Polynomial.IsDistinguishedAt.algEquivQuotient_symm_apply, Algebra.TensorProduct.quotIdealMapEquivTensorQuot_symm_tmul, DoubleQuot.quotQuotEquivQuotOfLEₐ_comp_mkₐ, Algebra.weaklyQuasiFiniteAt_iff, StandardEtalePresentation.toPresentation_σ', Algebra.Presentation.instFinitePresentationModelOfHasCoeffsOfFinite, AdicCompletion.evalₐ_liftAlgHom, AdicCompletion.surjective_evalₐ, instIsIntegralQuotientIdeal, AlgEquiv.prodQuotientOfIsIdempotentElem_apply_snd, AdicCompletion.mk_ofAlgEquiv_symm_eq_evalOneₐ, DoubleQuot.quotQuotEquivCommₐ_toRingEquiv, DoubleQuot.coe_quotQuotToQuotSupₐ, Algebra.Generators.naive_σ, trace_quotient_eq_trace_localization_quotient, DoubleQuot.quotQuotEquivQuotSupₐ_toRingEquiv, Algebra.Presentation.tensorModelOfHasCoeffsEquiv_symm_tmul, AlgEquiv.prodQuotientOfIsIdempotentElem_apply_fst, Algebra.TensorProduct.quotIdealMapEquivTensorQuot_mk, StandardEtalePresentation.toPresentation_algebra_algebraMap_apply, Algebra.FormallyUnramified.quotient, derivationToSquareZeroEquivLift_apply_coe_apply, AlgHom.ker_kerSquareLift, liftOfDerivationToSquareZero_mk_apply', Algebra.FormallySmooth.exists_adicCompletionEvalOneₐ_comp_eq, DoubleQuot.quotQuotEquivQuotOfLEₐ_toRingEquiv, AdicCompletion.evalₐ_of, AdjoinRoot.quotEquivQuotMap_symm_apply, StandardEtalePresentation.toPresentation_val, Algebra.Generators.compLocalizationAwayAlgHom_relation_eq_zero, Algebra.instEssFiniteTypeQuotientIdeal, AdicCompletion.evalOneₐ_surjective, AdicCompletion.factor_evalₐ_eq_eval, isStronglyTranscendental_mk_of_mem_minimalPrimes, AdicCompletion.evalₐ_comp_liftRingHom, cotangentEquivIdeal_symm_apply, AdicCompletion.evalₐ_mk, DoubleQuot.quotQuotEquivComm_comp_quotQuotMkₐ, DoubleQuot.quotQuotEquivComm_mk_mk, AdicCompletion.evalₐ_mkₐ, Algebra.Presentation.quotientEquiv_mk, DoubleQuot.coe_quotQuotEquivCommₐ, StandardEtalePresentation.toPresentation_relation, Algebra.PreSubmersivePresentation.ofHasCoeffs_val, PrimeSpectrum.mem_image_comap_zeroLocus_sdiff, DoubleQuot.quotQuotEquivQuotSup_quot_quot_algebraMap, Algebra.PreSubmersivePresentation.ofHasCoeffs_algebra_smul, AlgHom.kerSquareLift_mk, DoubleQuot.quotLeftToQuotSupₐ_toRingHom, DoubleQuot.quotQuotEquivQuotSupₐ_symm_toRingEquiv, Polynomial.IsDistinguishedAt.algEquivQuotient_apply, Algebra.Presentation.instFinitePresentationQuotientOfFinite, Algebra.FinitePresentation.quotient, Algebra.Generators.ker_naive, DoubleQuot.coe_liftSupQuotQuotMkₐ, AdicCompletion.evalOneₐ_liftAlgHom, AdicCompletion.evalₐ_liftRingHom, Algebra.Presentation.mem_ker_naive, Factors.piQuotientEquiv_map, derivationQuotKerSq_mk, DoubleQuot.quotQuotEquivComm_algebraMap, Algebra.Presentation.tensorModelOfHasCoeffsInv_aeval_val
instAlgebraQuotientComapRingHomAlgebraMap 📖CompOp
4 mathmath: AlgHom.IsArithFrobAt.restrict_injective, Algebra.IsIntegral.quotient, AlgHom.IsArithFrobAt.restrict_mk, AlgHom.IsArithFrobAt.restrict_apply
kerLiftAlg 📖CompOp
3 mathmath: kerLiftAlg_injective, kerLiftAlg_toRingHom, kerLiftAlg_mk
powQuotPowSuccEquivMapMkPowSuccPow 📖CompOp
powQuotPowSuccLinearEquivMapMkPowSuccPow 📖CompOp
quotientAlgebra 📖CompOp
1 mathmath: algebraMap_quotient_injective
quotientEquiv 📖CompOp
5 mathmath: quotientEquiv_symm_apply, quotientEquiv_symm_mk, PowerBasis.quotientEquivQuotientMinpolyMap_symm_apply, quotientEquiv_apply, quotientEquiv_mk
quotientEquivAlg 📖CompOp
2 mathmath: quotientEquivAlg_mk, quotientEquivAlg_symm
quotientEquivAlgOfEq 📖CompOp
6 mathmath: PowerSeries.IsWeierstrassFactorizationAt.algEquivQuotient_apply, quotientEquivAlgOfEq_coe_eq_factorₐ, PowerSeries.IsWeierstrassFactorizationAt.algEquivQuotient_symm_apply, quotientEquivAlgOfEq_coe_eq_factor, quotientEquivAlgOfEq_mk, quotientEquivAlgOfEq_symm
quotientInfEquivQuotientProd 📖CompOp
4 mathmath: quotientInfEquivQuotientProd_snd, quotientInfEquivQuotientProd_fst, fst_comp_quotientInfEquivQuotientProd, snd_comp_quotientInfEquivQuotientProd
quotientInfRingEquivPiQuotient 📖CompOp
quotientInfToPiQuotient 📖CompOp
4 mathmath: quotientInfToPiQuotient_inj, quotientInfToPiQuotient_surj, quotientInfToPiQuotient_mk', quotientInfToPiQuotient_mk
quotientKerAlgEquivOfRightInverse 📖CompOp
2 mathmath: quotientKerAlgEquivOfRightInverse_symm_apply, quotientKerAlgEquivOfRightInverse_apply
quotientKerAlgEquivOfSurjective 📖CompOp
3 mathmath: quotientKerAlgEquivOfSurjective_apply, quotientKerAlgEquivOfSurjective_symm_apply, quotientKerAlgEquivOfSurjective_mk
quotientKerEquivRange 📖CompOp
quotientMap 📖CompOp
18 mathmath: IsLocalization.surjective_quotientMap_of_maximal_of_localization, quotientEquiv_symm_apply, quotientMap_comp_mk, PowerBasis.quotientEquivQuotientMinpolyMap_apply, injective_quotient_le_comap_map, comp_quotientMap_eq_of_comp_eq, quotientMap_mk, AlgebraicGeometry.Scheme.IdealSheafData.isLocalization_away, quotientEquiv_apply, quotientMap_injective', RingHom.IsIntegral.quotient, quotientMap_surjective, ker_quotientMap_mk, quotientMap_algebraMap, quotientMap_injective, quotient_mk_maps_eq, isIntegral_quotientMap_iff, Polynomial.isIntegral_isLocalization_polynomial_quotient
quotientMapₐ 📖CompOp
4 mathmath: PowerSeries.IsWeierstrassFactorizationAt.algEquivQuotient_apply, quotient_map_comp_mkₐ, quotient_map_mkₐ, Polynomial.IsDistinguishedAt.algEquivQuotient_apply
quotientMulEquivQuotientProd 📖CompOp
4 mathmath: quotientMulEquivQuotientProd_snd, fst_comp_quotientMulEquivQuotientProd, snd_comp_quotientMulEquivQuotientProd, quotientMulEquivQuotientProd_fst

Theorems

NameKindAssumesProvesValidatesDepends On
algebraMap_quotient_injective 📖mathematicalHasQuotient.Quotient
Ideal
CommSemiring.toSemiring
CommRing.toCommSemiring
instHasQuotient_1
comap
RingHom
Semiring.toNonAssocSemiring
Ring.toSemiring
RingHom.instFunLike
algebraMap
RingHom.instRingHomClass
instHasQuotient
DFunLike.coe
Quotient.commSemiring
Quotient.ring
quotientAlgebra
RingHom.instRingHomClass
Quotient.eq
instIsTwoSided_1
map_sub
RingHomClass.toAddMonoidHomClass
bot_quotient_isMaximal_iff 📖mathematicalIsMaximal
HasQuotient.Quotient
Ideal
Ring.toSemiring
instHasQuotient
Quotient.ring
Bot.bot
Submodule.instBot
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
RingHom.instRingHomClass
comap_isMaximal_of_surjective
Quotient.mk_surjective
mk_ker
bot_isMaximal
comap_map_mk 📖mathematicalIdeal
Ring.toSemiring
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
comap
HasQuotient.Quotient
instHasQuotient
RingHom
Quotient.ring
RingHom.instFunLike
RingHom.instRingHomClass
map
RingHom.instRingHomClass
comap_map_quotientMk
comap_map_quotientMk 📖mathematicalcomap
HasQuotient.Quotient
Ideal
Ring.toSemiring
instHasQuotient
RingHom
Semiring.toNonAssocSemiring
Quotient.ring
RingHom.instFunLike
RingHom.instRingHomClass
map
SemilatticeSup.toMax
Lattice.toSemilatticeSup
ConditionallyCompleteLattice.toLattice
CompleteLattice.toConditionallyCompleteLattice
Submodule.completeLattice
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toModule
ext
RingHom.instRingHomClass
sup_comm
comp_quotientMap_eq_of_comp_eq 📖mathematicalRingHom.comp
Semiring.toNonAssocSemiring
Ring.toSemiring
HasQuotient.Quotient
Ideal
instHasQuotient
comap
RingHom
RingHom.instFunLike
RingHom.instRingHomClass
Quotient.ring
instIsTwoSidedComap
quotientMap
le_rfl
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toModule
le_of_eq
trans
IsPreorder.toIsTrans
IsEquiv.toIsPreorder
eq_isEquiv
comap_comap
RingHom.ext
RingHom.instRingHomClass
instIsTwoSidedComap
le_rfl
le_of_eq
trans
IsPreorder.toIsTrans
IsEquiv.toIsPreorder
eq_isEquiv
comap_comap
Quotient.mk_surjective
RingHom.congr_arg
RingHom.comp_apply
exists_forall_sub_mem_ideal 📖mathematicalPairwise
Function.onFun
Ideal
CommSemiring.toSemiring
CommRing.toCommSemiring
IsCoprime
IdemCommSemiring.toCommSemiring
instIdemCommSemiring
SetLike.instMembership
Submodule.setLike
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
AddGroupWithOne.toAddGroup
Ring.toAddGroupWithOne
CommRing.toRing
instIsTwoSided_1
pi_quotient_surjective
Submodule.Quotient.eq
fst_comp_quotientInfEquivQuotientProd 📖mathematicalIsCoprime
Ideal
CommSemiring.toSemiring
CommRing.toCommSemiring
IdemCommSemiring.toCommSemiring
instIdemCommSemiring
RingHom.comp
HasQuotient.Quotient
instHasQuotient_1
Submodule.instMin
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Quotient.semiring
Prod.instNonAssocSemiring
RingHom.fst
RingHomClass.toRingHom
RingEquiv
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Quotient.commRing
Prod.instMul
Distrib.toAdd
Prod.instAdd
EquivLike.toFunLike
RingEquiv.instEquivLike
RingEquivClass.toRingHomClass
RingEquiv.instRingEquivClass
quotientInfEquivQuotientProd
Quotient.factor
CommRing.toRing
Ring.toSemiring
SemilatticeInf.toMin
Lattice.toSemilatticeInf
ConditionallyCompleteLattice.toLattice
CompleteLattice.toConditionallyCompleteLattice
Submodule.completeLattice
instIsTwoSided_1
inf_le_left
Quotient.ringHom_ext
instIsTwoSided_1
RingEquivClass.toRingHomClass
RingEquiv.instRingEquivClass
inf_le_left
RingHom.ext
fst_comp_quotientMulEquivQuotientProd 📖mathematicalIsCoprime
Ideal
CommSemiring.toSemiring
CommRing.toCommSemiring
IdemCommSemiring.toCommSemiring
instIdemCommSemiring
RingHom.comp
HasQuotient.Quotient
instHasQuotient_1
Submodule.mul
Semiring.toModule
IsScalarTower.right
Algebra.id
Semiring.toNonAssocSemiring
Quotient.semiring
Prod.instNonAssocSemiring
RingHom.fst
RingHomClass.toRingHom
RingEquiv
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Quotient.commRing
Prod.instMul
Distrib.toAdd
Prod.instAdd
EquivLike.toFunLike
RingEquiv.instEquivLike
RingEquivClass.toRingHomClass
RingEquiv.instRingEquivClass
quotientMulEquivQuotientProd
Quotient.factor
CommRing.toRing
Ring.toSemiring
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Module.toDistribMulAction
instIsTwoSided_1
mul_le_right
Quotient.ringHom_ext
IsScalarTower.right
instIsTwoSided_1
RingEquivClass.toRingHomClass
RingEquiv.instRingEquivClass
IsScalarTower.left
mul_le_right
RingHom.ext
injective_lift_iff 📖mathematicalDFunLike.coe
RingHom
Semiring.toNonAssocSemiring
Ring.toSemiring
RingHom.instFunLike
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonAssocSemiring.toNonUnitalNonAssocSemiring
HasQuotient.Quotient
Ideal
instHasQuotient
Quotient.ring
Quotient.lift
RingHom.ker
RingHom.instRingHomClass
RingHom.instRingHomClass
RingHom.injective_iff_ker_eq_bot
ker_quotient_lift
map_eq_bot_iff_le_ker
mk_ker
le_antisymm
le_refl
isPrime_map_quotientMk_of_isPrime 📖mathematicalIdeal
Ring.toSemiring
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
IsPrime
HasQuotient.Quotient
instHasQuotient
Quotient.ring
map
RingHom
RingHom.instFunLike
map_isPrime_of_surjective
RingHom.instRingHomClass
Quotient.mk_surjective
mk_ker
kerLiftAlg_injective 📖mathematicalHasQuotient.Quotient
Ideal
Ring.toSemiring
instHasQuotient
RingHom.ker
AlgHom
AlgHom.funLike
AlgHomClass.toRingHomClass
AlgHom.algHomClass
DFunLike.coe
Quotient.ring
RingHom.instIsTwoSidedKer
Quotient.algebra
kerLiftAlg
RingHom.kerLift_injective
AlgHomClass.toRingHomClass
AlgHom.algHomClass
kerLiftAlg_mk 📖mathematicalDFunLike.coe
AlgHom
HasQuotient.Quotient
Ideal
Ring.toSemiring
instHasQuotient
RingHom.ker
AlgHom.funLike
AlgHomClass.toRingHomClass
AlgHom.algHomClass
Quotient.ring
RingHom.instIsTwoSidedKer
Quotient.algebra
kerLiftAlg
RingHom
Semiring.toNonAssocSemiring
RingHom.instFunLike
AlgHomClass.toRingHomClass
AlgHom.algHomClass
RingHom.instIsTwoSidedKer
kerLiftAlg_toRingHom 📖mathematicalRingHomClass.toRingHom
AlgHom
HasQuotient.Quotient
Ideal
Ring.toSemiring
instHasQuotient
RingHom.ker
AlgHom.funLike
AlgHomClass.toRingHomClass
AlgHom.algHomClass
Quotient.ring
RingHom.instIsTwoSidedKer
Quotient.algebra
Semiring.toNonAssocSemiring
kerLiftAlg
RingHom.kerLift
AlgHomClass.toRingHomClass
AlgHom.algHomClass
RingHom.instIsTwoSidedKer
ker_Pi_Quotient_mk 📖mathematicalIsTwoSided
Ring.toSemiring
RingHom.ker
RingHom
Semiring.toNonAssocSemiring
Pi.nonAssocSemiring
HasQuotient.Quotient
Ideal
instHasQuotient
Quotient.ring
Pi.semiring
RingHom.instFunLike
RingHom.instRingHomClass
Pi.ringHom
iInf
Submodule.instInfSet
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toModule
RingHom.instRingHomClass
Pi.ker_ringHom
mk_ker
ker_quotientMap_mk 📖mathematicalRingHom.ker
HasQuotient.Quotient
Ideal
Ring.toSemiring
instHasQuotient
Quotient.ring
map
RingHom
Semiring.toNonAssocSemiring
RingHom.instFunLike
instIsTwoSidedMapRingHomOfRingHomSurjective
Quotient.instRingHomSurjectiveQuotientMk
RingHom.instRingHomClass
quotientMap
le_comap_map
instIsTwoSidedMapRingHomOfRingHomSurjective
Quotient.instRingHomSurjectiveQuotientMk
RingHom.instRingHomClass
le_comap_map
quotientMap.eq_1
ker_quotient_lift
RingHom.comap_ker
mk_ker
comap_map_of_surjective
Quotient.mk_surjective
RingHom.ker_eq_comap_bot
map_sup
map_quotient_self
bot_sup_eq
ker_quotient_lift 📖mathematicalIdeal
Ring.toSemiring
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
RingHom.ker
RingHom
RingHom.instFunLike
RingHom.instRingHomClass
HasQuotient.Quotient
instHasQuotient
Quotient.ring
Quotient.lift
map
RingHom.instRingHomClass
ext
Quotient.mk_surjective
mem_map_iff_of_surjective
RingHom.mem_ker
map_mk_eq_bot_of_le 📖mathematicalIdeal
Ring.toSemiring
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
map
HasQuotient.Quotient
instHasQuotient
RingHom
Quotient.ring
RingHom.instFunLike
Bot.bot
Submodule.instBot
RingHom.instRingHomClass
map_eq_bot_iff_le_ker
mk_ker
map_quotient_self 📖mathematicalmap
HasQuotient.Quotient
Ideal
Ring.toSemiring
instHasQuotient
RingHom
Semiring.toNonAssocSemiring
Quotient.ring
RingHom.instFunLike
Bot.bot
Submodule.instBot
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toModule
eq_bot_iff
RingHom.instRingHomClass
map_le_iff_le_comap
Submodule.mem_bot
Quotient.eq_zero_iff_mem
mem_quotient_iff_mem 📖mathematicalIdeal
Ring.toSemiring
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
HasQuotient.Quotient
instHasQuotient
Quotient.ring
SetLike.instMembership
Submodule.setLike
map
RingHom
RingHom.instFunLike
DFunLike.coe
mem_quotient_iff_mem_sup
sup_eq_left
mem_quotient_iff_mem_sup 📖mathematicalHasQuotient.Quotient
Ideal
Ring.toSemiring
instHasQuotient
Quotient.ring
SetLike.instMembership
Submodule.setLike
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
map
RingHom
RingHom.instFunLike
DFunLike.coe
SemilatticeSup.toMax
Lattice.toSemilatticeSup
ConditionallyCompleteLattice.toLattice
CompleteLattice.toConditionallyCompleteLattice
Submodule.completeLattice
RingHom.instRingHomClass
mem_comap
comap_map_of_surjective
Quotient.mk_surjective
RingHom.ker_eq_comap_bot
mk_ker
mk_ker 📖mathematicalRingHom.ker
HasQuotient.Quotient
Ideal
Ring.toSemiring
instHasQuotient
RingHom
Semiring.toNonAssocSemiring
Quotient.ring
RingHom.instFunLike
RingHom.instRingHomClass
ext
RingHom.instRingHomClass
RingHom.ker.eq_1
mem_comap
Submodule.mem_bot
Quotient.eq_zero_iff_mem
pi_mkQ_surjective 📖mathematicalPairwise
Function.onFun
Ideal
CommSemiring.toSemiring
CommRing.toCommSemiring
IsCoprime
IdemCommSemiring.toCommSemiring
instIdemCommSemiring
DFunLike.coe
LinearMap
Ring.toSemiring
CommRing.toRing
RingHom.id
Semiring.toNonAssocSemiring
AddCommGroup.toAddCommMonoid
Ring.toAddCommGroup
Pi.addCommMonoid
HasQuotient.Quotient
Submodule
Semiring.toModule
Submodule.hasQuotient
NonUnitalNonAssocSemiring.toAddCommMonoid
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Quotient.commRing
Pi.module
Submodule.Quotient.module
LinearMap.instFunLike
LinearMap.pi
Submodule.mkQ
instIsTwoSided_1
pi_quotient_surjective
pi_quotient_surjective 📖mathematicalPairwise
Function.onFun
Ideal
CommSemiring.toSemiring
CommRing.toCommSemiring
IsCoprime
IdemCommSemiring.toCommSemiring
instIdemCommSemiring
DFunLike.coe
RingHom
HasQuotient.Quotient
Ring.toSemiring
CommRing.toRing
instHasQuotient
Semiring.toNonAssocSemiring
Quotient.ring
instIsTwoSided_1
RingHom.instFunLike
instIsTwoSidedIInf
instIsTwoSided_1
quotientInfToPiQuotient_surj
Quotient.mk_surjective
quotientEquivAlgOfEq_coe_eq_factor 📖mathematicalRingHomClass.toRingHom
AlgEquiv
HasQuotient.Quotient
Ideal
Ring.toSemiring
instHasQuotient
Quotient.ring
Quotient.algebra
AlgEquiv.instFunLike
Semiring.toNonAssocSemiring
AlgHomClass.toRingHomClass
AlgEquivClass.toAlgHomClass
AlgEquiv.instEquivLike
AlgEquiv.instAlgEquivClass
quotientEquivAlgOfEq
Quotient.factor
le_of_eq
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toModule
AlgHomClass.toRingHomClass
AlgEquivClass.toAlgHomClass
AlgEquiv.instAlgEquivClass
quotientEquivAlgOfEq_coe_eq_factorₐ 📖mathematicalAlgHomClass.toAlgHom
HasQuotient.Quotient
Ideal
Ring.toSemiring
instHasQuotient
Quotient.ring
Quotient.algebra
AlgEquiv
AlgEquiv.instFunLike
AlgEquivClass.toAlgHomClass
AlgEquiv.instEquivLike
AlgEquiv.instAlgEquivClass
quotientEquivAlgOfEq
Quotient.factorₐ
le_of_eq
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
AlgEquivClass.toAlgHomClass
AlgEquiv.instAlgEquivClass
quotientEquivAlgOfEq_mk 📖mathematicalDFunLike.coe
AlgEquiv
HasQuotient.Quotient
Ideal
Ring.toSemiring
instHasQuotient
Quotient.ring
Quotient.algebra
AlgEquiv.instFunLike
quotientEquivAlgOfEq
RingHom
Semiring.toNonAssocSemiring
RingHom.instFunLike
quotientEquivAlgOfEq_symm 📖mathematicalAlgEquiv.symm
HasQuotient.Quotient
Ideal
Ring.toSemiring
instHasQuotient
Quotient.ring
Quotient.algebra
quotientEquivAlgOfEq
AlgEquiv.ext
quotientEquivAlg_mk 📖mathematicalmap
RingHom
Semiring.toNonAssocSemiring
Ring.toSemiring
RingHom.instFunLike
RingHomClass.toRingHom
AlgEquiv
AlgEquiv.instFunLike
AlgHomClass.toRingHomClass
AlgEquivClass.toAlgHomClass
AlgEquiv.instEquivLike
AlgEquiv.instAlgEquivClass
DFunLike.coe
HasQuotient.Quotient
Ideal
instHasQuotient
Quotient.ring
Quotient.algebra
quotientEquivAlg
AlgHomClass.toRingHomClass
AlgEquivClass.toAlgHomClass
AlgEquiv.instAlgEquivClass
quotientEquivAlg_symm 📖mathematicalmap
RingHom
Semiring.toNonAssocSemiring
Ring.toSemiring
RingHom.instFunLike
RingHomClass.toRingHom
AlgEquiv
AlgEquiv.instFunLike
AlgHomClass.toRingHomClass
AlgEquivClass.toAlgHomClass
AlgEquiv.instEquivLike
AlgEquiv.instAlgEquivClass
AlgEquiv.symm
HasQuotient.Quotient
Ideal
instHasQuotient
Quotient.ring
Quotient.algebra
quotientEquivAlg
AlgHomClass.toRingHomClass
AlgEquivClass.toAlgHomClass
AlgEquiv.instAlgEquivClass
quotientEquiv_apply 📖mathematicalmap
RingHom
Semiring.toNonAssocSemiring
Ring.toSemiring
RingHom.instFunLike
RingHomClass.toRingHom
RingEquiv
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
Distrib.toAdd
EquivLike.toFunLike
RingEquiv.instEquivLike
RingEquivClass.toRingHomClass
RingEquiv.instRingEquivClass
DFunLike.coe
HasQuotient.Quotient
Ideal
instHasQuotient
Quotient.ring
quotientEquiv
OneHom.toFun
MulOne.toOne
MulOneClass.toMulOne
MulZeroOneClass.toMulOneClass
NonAssocSemiring.toMulZeroOneClass
MonoidHom.toOneHom
RingHom.toMonoidHom
quotientMap
RingEquivClass.toRingHomClass
RingEquiv.instRingEquivClass
quotientEquiv_mk 📖mathematicalmap
RingHom
Semiring.toNonAssocSemiring
Ring.toSemiring
RingHom.instFunLike
RingHomClass.toRingHom
RingEquiv
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
Distrib.toAdd
EquivLike.toFunLike
RingEquiv.instEquivLike
RingEquivClass.toRingHomClass
RingEquiv.instRingEquivClass
DFunLike.coe
HasQuotient.Quotient
Ideal
instHasQuotient
Quotient.ring
quotientEquiv
RingEquivClass.toRingHomClass
RingEquiv.instRingEquivClass
quotientEquiv_symm_apply 📖mathematicalmap
RingHom
Semiring.toNonAssocSemiring
Ring.toSemiring
RingHom.instFunLike
RingHomClass.toRingHom
RingEquiv
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
Distrib.toAdd
EquivLike.toFunLike
RingEquiv.instEquivLike
RingEquivClass.toRingHomClass
RingEquiv.instRingEquivClass
DFunLike.coe
HasQuotient.Quotient
Ideal
instHasQuotient
Quotient.ring
RingEquiv.symm
quotientEquiv
quotientMap
RingEquivClass.toRingHomClass
RingEquiv.instRingEquivClass
quotientEquiv_symm_mk 📖mathematicalmap
RingHom
Semiring.toNonAssocSemiring
Ring.toSemiring
RingHom.instFunLike
RingHomClass.toRingHom
RingEquiv
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
Distrib.toAdd
EquivLike.toFunLike
RingEquiv.instEquivLike
RingEquivClass.toRingHomClass
RingEquiv.instRingEquivClass
DFunLike.coe
HasQuotient.Quotient
Ideal
instHasQuotient
Quotient.ring
RingEquiv.symm
quotientEquiv
RingEquivClass.toRingHomClass
RingEquiv.instRingEquivClass
quotientInfEquivQuotientProd_fst 📖mathematicalIsCoprime
Ideal
CommSemiring.toSemiring
CommRing.toCommSemiring
IdemCommSemiring.toCommSemiring
instIdemCommSemiring
HasQuotient.Quotient
instHasQuotient_1
DFunLike.coe
RingEquiv
Submodule.instMin
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Quotient.commRing
Prod.instMul
Distrib.toAdd
Prod.instAdd
EquivLike.toFunLike
RingEquiv.instEquivLike
quotientInfEquivQuotientProd
RingHom
Ring.toSemiring
CommRing.toRing
instHasQuotient
SemilatticeInf.toMin
Lattice.toSemilatticeInf
ConditionallyCompleteLattice.toLattice
CompleteLattice.toConditionallyCompleteLattice
Submodule.completeLattice
Quotient.ring
instIsTwoSided_1
RingHom.instFunLike
Quotient.factor
inf_le_left
instIsTwoSided_1
inf_le_left
quotientInfEquivQuotientProd_snd 📖mathematicalIsCoprime
Ideal
CommSemiring.toSemiring
CommRing.toCommSemiring
IdemCommSemiring.toCommSemiring
instIdemCommSemiring
HasQuotient.Quotient
instHasQuotient_1
DFunLike.coe
RingEquiv
Submodule.instMin
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Quotient.commRing
Prod.instMul
Distrib.toAdd
Prod.instAdd
EquivLike.toFunLike
RingEquiv.instEquivLike
quotientInfEquivQuotientProd
RingHom
Ring.toSemiring
CommRing.toRing
instHasQuotient
SemilatticeInf.toMin
Lattice.toSemilatticeInf
ConditionallyCompleteLattice.toLattice
CompleteLattice.toConditionallyCompleteLattice
Submodule.completeLattice
Quotient.ring
instIsTwoSided_1
RingHom.instFunLike
Quotient.factor
inf_le_right
instIsTwoSided_1
inf_le_right
quotientInfToPiQuotient_inj 📖mathematicalIsTwoSided
Ring.toSemiring
HasQuotient.Quotient
Ideal
instHasQuotient
iInf
Submodule.instInfSet
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
DFunLike.coe
RingHom
Quotient.ring
instIsTwoSidedIInf
Pi.nonAssocSemiring
RingHom.instFunLike
quotientInfToPiQuotient
instIsTwoSidedIInf
quotientInfToPiQuotient.eq_1
RingHom.instRingHomClass
injective_lift_iff
quotientInfToPiQuotient_mk 📖mathematicalIsTwoSided
Ring.toSemiring
DFunLike.coe
RingHom
HasQuotient.Quotient
Ideal
instHasQuotient
iInf
Submodule.instInfSet
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Quotient.ring
instIsTwoSidedIInf
Pi.nonAssocSemiring
RingHom.instFunLike
quotientInfToPiQuotient
instIsTwoSidedIInf
quotientInfToPiQuotient_mk' 📖mathematicalIsTwoSided
Ring.toSemiring
DFunLike.coe
RingHom
HasQuotient.Quotient
Ideal
instHasQuotient
iInf
Submodule.instInfSet
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Quotient.ring
instIsTwoSidedIInf
Pi.nonAssocSemiring
RingHom.instFunLike
quotientInfToPiQuotient
instIsTwoSidedIInf
quotientInfToPiQuotient_surj 📖mathematicalPairwise
Function.onFun
Ideal
CommSemiring.toSemiring
CommRing.toCommSemiring
IsCoprime
IdemCommSemiring.toCommSemiring
instIdemCommSemiring
HasQuotient.Quotient
Ring.toSemiring
CommRing.toRing
instHasQuotient
iInf
Submodule.instInfSet
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
DFunLike.coe
RingHom
Quotient.ring
instIsTwoSidedIInf
instIsTwoSided_1
Pi.nonAssocSemiring
RingHom.instFunLike
quotientInfToPiQuotient
nonempty_fintype
instIsTwoSidedIInf
instIsTwoSided_1
isCoprime_iff_exists
isCoprime_biInf
iInf_congr_Prop
eq_sub_of_add_eq'
map_sub
RingHomClass.toAddMonoidHomClass
RingHom.instRingHomClass
map_one
MonoidHomClass.toOneHomClass
MonoidWithZeroHomClass.toMonoidHomClass
RingHomClass.toMonoidWithZeroHomClass
Quotient.eq_zero_iff_mem
sub_zero
quotientInfToPiQuotient_mk'
map_sum
Fintype.sum_eq_single
map_mul
NonUnitalRingHomClass.toMulHomClass
RingHomClass.toNonUnitalRingHomClass
MulZeroClass.mul_zero
mul_one
Quotient.mk_surjective
quotientKerAlgEquivOfRightInverse_apply 📖mathematicalDFunLike.coe
AlgHom
Ring.toSemiring
AlgHom.funLike
AlgEquiv
HasQuotient.Quotient
Ideal
instHasQuotient
RingHom.ker
AlgHomClass.toRingHomClass
AlgHom.algHomClass
Quotient.ring
RingHom.instIsTwoSidedKer
Quotient.algebra
AlgEquiv.instFunLike
quotientKerAlgEquivOfRightInverse
RingHom
Semiring.toNonAssocSemiring
RingHom.instFunLike
RingHomClass.toRingHom
AlgHom.toRingHom
RingHom.kerLift
AlgHomClass.toRingHomClass
AlgHom.algHomClass
RingHom.instIsTwoSidedKer
quotientKerAlgEquivOfRightInverse_symm_apply 📖mathematicalDFunLike.coe
AlgHom
Ring.toSemiring
AlgHom.funLike
AlgEquiv
HasQuotient.Quotient
Ideal
instHasQuotient
RingHom.ker
AlgHomClass.toRingHomClass
AlgHom.algHomClass
Quotient.ring
RingHom.instIsTwoSidedKer
Quotient.algebra
AlgEquiv.instFunLike
AlgEquiv.symm
quotientKerAlgEquivOfRightInverse
RingHom
Semiring.toNonAssocSemiring
RingHom.instFunLike
RingHomClass.toRingHom
AlgHom.toRingHom
AlgHomClass.toRingHomClass
AlgHom.algHomClass
RingHom.instIsTwoSidedKer
quotientKerAlgEquivOfSurjective_apply 📖mathematicalDFunLike.coe
AlgHom
Ring.toSemiring
AlgHom.funLike
AlgEquiv
HasQuotient.Quotient
Ideal
instHasQuotient
RingHom.ker
AlgHomClass.toRingHomClass
AlgHom.algHomClass
Quotient.ring
RingHom.instIsTwoSidedKer
Quotient.algebra
AlgEquiv.instFunLike
quotientKerAlgEquivOfSurjective
RingHom
Semiring.toNonAssocSemiring
RingHom.instFunLike
RingHomClass.toRingHom
AlgHom.toRingHom
RingHom.kerLift
AlgHomClass.toRingHomClass
AlgHom.algHomClass
RingHom.instIsTwoSidedKer
quotientKerAlgEquivOfSurjective_mk 📖mathematicalDFunLike.coe
AlgHom
Ring.toSemiring
AlgHom.funLike
AlgEquiv
HasQuotient.Quotient
Ideal
instHasQuotient
RingHom.ker
AlgHomClass.toRingHomClass
AlgHom.algHomClass
Quotient.ring
RingHom.instIsTwoSidedKer
Quotient.algebra
AlgEquiv.instFunLike
quotientKerAlgEquivOfSurjective
RingHom
Semiring.toNonAssocSemiring
RingHom.instFunLike
AlgHomClass.toRingHomClass
AlgHom.algHomClass
RingHom.instIsTwoSidedKer
quotientKerAlgEquivOfSurjective_symm_apply 📖mathematicalDFunLike.coe
AlgHom
Ring.toSemiring
AlgHom.funLike
AlgEquiv
HasQuotient.Quotient
Ideal
instHasQuotient
RingHom.ker
AlgHomClass.toRingHomClass
AlgHom.algHomClass
Quotient.ring
RingHom.instIsTwoSidedKer
Quotient.algebra
AlgEquiv.instFunLike
AlgEquiv.symm
quotientKerAlgEquivOfSurjective
RingHom
Semiring.toNonAssocSemiring
RingHom.instFunLike
AlgEquiv.injective
AlgHomClass.toRingHomClass
AlgHom.algHomClass
RingHom.instIsTwoSidedKer
AlgEquiv.apply_symm_apply
quotientMap_algebraMap 📖mathematicalIdeal
Ring.toSemiring
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
comap
RingHom
RingHom.instFunLike
RingHom.instRingHomClass
DFunLike.coe
HasQuotient.Quotient
instHasQuotient
Quotient.ring
quotientMap
CommSemiring.toSemiring
algebraMap
Quotient.algebra
RingHom.instRingHomClass
quotientMap_comp_mk 📖mathematicalIdeal
Ring.toSemiring
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
comap
RingHom
RingHom.instFunLike
RingHom.instRingHomClass
RingHom.comp
HasQuotient.Quotient
instHasQuotient
Quotient.ring
quotientMap
RingHom.instRingHomClass
RingHom.ext
quotientMap_injective 📖mathematicalHasQuotient.Quotient
Ideal
Ring.toSemiring
instHasQuotient
comap
RingHom
Semiring.toNonAssocSemiring
RingHom.instFunLike
RingHom.instRingHomClass
DFunLike.coe
Quotient.ring
instIsTwoSidedComap
quotientMap
le_rfl
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toModule
quotientMap_injective'
RingHom.instRingHomClass
instIsTwoSidedComap
le_rfl
quotientMap_injective' 📖mathematicalIdeal
Ring.toSemiring
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
comap
RingHom
RingHom.instFunLike
RingHom.instRingHomClass
HasQuotient.Quotient
instHasQuotient
DFunLike.coe
Quotient.ring
quotientMap
RingHom.instRingHomClass
injective_iff_map_eq_zero
RingHomClass.toAddMonoidHomClass
Quotient.mk_surjective
Quotient.eq_zero_iff_mem
quotientMap_mk 📖mathematicalIdeal
Ring.toSemiring
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
comap
RingHom
RingHom.instFunLike
RingHom.instRingHomClass
DFunLike.coe
HasQuotient.Quotient
instHasQuotient
Quotient.ring
quotientMap
RingHom.instRingHomClass
quotientMap_surjective 📖mathematicalIdeal
Ring.toSemiring
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
comap
RingHom
RingHom.instFunLike
RingHom.instRingHomClass
DFunLike.coe
HasQuotient.Quotient
instHasQuotient
Quotient.ring
quotientMap
RingHom.instRingHomClass
Quotient.mk_surjective
quotientMulEquivQuotientProd_fst 📖mathematicalIsCoprime
Ideal
CommSemiring.toSemiring
CommRing.toCommSemiring
IdemCommSemiring.toCommSemiring
instIdemCommSemiring
HasQuotient.Quotient
instHasQuotient_1
DFunLike.coe
RingEquiv
Submodule.mul
Semiring.toModule
IsScalarTower.right
Algebra.id
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Quotient.commRing
Prod.instMul
Distrib.toAdd
Prod.instAdd
EquivLike.toFunLike
RingEquiv.instEquivLike
quotientMulEquivQuotientProd
RingHom
Ring.toSemiring
CommRing.toRing
instHasQuotient
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Module.toDistribMulAction
Quotient.ring
instIsTwoSided_1
RingHom.instFunLike
Quotient.factor
mul_le_right
IsScalarTower.right
IsScalarTower.left
instIsTwoSided_1
mul_le_right
quotientMulEquivQuotientProd_snd 📖mathematicalIsCoprime
Ideal
CommSemiring.toSemiring
CommRing.toCommSemiring
IdemCommSemiring.toCommSemiring
instIdemCommSemiring
HasQuotient.Quotient
instHasQuotient_1
DFunLike.coe
RingEquiv
Submodule.mul
Semiring.toModule
IsScalarTower.right
Algebra.id
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Quotient.commRing
Prod.instMul
Distrib.toAdd
Prod.instAdd
EquivLike.toFunLike
RingEquiv.instEquivLike
quotientMulEquivQuotientProd
RingHom
Ring.toSemiring
CommRing.toRing
instHasQuotient
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Module.toDistribMulAction
Quotient.ring
instIsTwoSided_1
RingHom.instFunLike
Quotient.factor
mul_le_left
IsScalarTower.right
IsScalarTower.left
instIsTwoSided_1
mul_le_left
quotient_map_comp_mkₐ 📖mathematicalIdeal
Ring.toSemiring
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
comap
AlgHom
AlgHom.funLike
AlgHomClass.toRingHomClass
AlgHom.algHomClass
AlgHom.comp
HasQuotient.Quotient
instHasQuotient
Quotient.ring
Quotient.algebra
quotientMapₐ
Quotient.mkₐ
AlgHomClass.toRingHomClass
AlgHom.algHomClass
AlgHom.ext
quotient_map_mkₐ 📖mathematicalIdeal
Ring.toSemiring
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
comap
AlgHom
AlgHom.funLike
AlgHomClass.toRingHomClass
AlgHom.algHomClass
DFunLike.coe
HasQuotient.Quotient
instHasQuotient
Quotient.ring
Quotient.algebra
quotientMapₐ
RingHom
RingHom.instFunLike
Quotient.mkₐ
AlgHomClass.toRingHomClass
AlgHom.algHomClass
snd_comp_quotientInfEquivQuotientProd 📖mathematicalIsCoprime
Ideal
CommSemiring.toSemiring
CommRing.toCommSemiring
IdemCommSemiring.toCommSemiring
instIdemCommSemiring
RingHom.comp
HasQuotient.Quotient
instHasQuotient_1
Submodule.instMin
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Quotient.semiring
Prod.instNonAssocSemiring
RingHom.snd
RingHomClass.toRingHom
RingEquiv
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Quotient.commRing
Prod.instMul
Distrib.toAdd
Prod.instAdd
EquivLike.toFunLike
RingEquiv.instEquivLike
RingEquivClass.toRingHomClass
RingEquiv.instRingEquivClass
quotientInfEquivQuotientProd
Quotient.factor
CommRing.toRing
Ring.toSemiring
SemilatticeInf.toMin
Lattice.toSemilatticeInf
ConditionallyCompleteLattice.toLattice
CompleteLattice.toConditionallyCompleteLattice
Submodule.completeLattice
instIsTwoSided_1
inf_le_right
Quotient.ringHom_ext
instIsTwoSided_1
RingEquivClass.toRingHomClass
RingEquiv.instRingEquivClass
inf_le_right
RingHom.ext
snd_comp_quotientMulEquivQuotientProd 📖mathematicalIsCoprime
Ideal
CommSemiring.toSemiring
CommRing.toCommSemiring
IdemCommSemiring.toCommSemiring
instIdemCommSemiring
RingHom.comp
HasQuotient.Quotient
instHasQuotient_1
Submodule.mul
Semiring.toModule
IsScalarTower.right
Algebra.id
Semiring.toNonAssocSemiring
Quotient.semiring
Prod.instNonAssocSemiring
RingHom.snd
RingHomClass.toRingHom
RingEquiv
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Quotient.commRing
Prod.instMul
Distrib.toAdd
Prod.instAdd
EquivLike.toFunLike
RingEquiv.instEquivLike
RingEquivClass.toRingHomClass
RingEquiv.instRingEquivClass
quotientMulEquivQuotientProd
Quotient.factor
CommRing.toRing
Ring.toSemiring
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Module.toDistribMulAction
instIsTwoSided_1
mul_le_left
Quotient.ringHom_ext
IsScalarTower.right
instIsTwoSided_1
RingEquivClass.toRingHomClass
RingEquiv.instRingEquivClass
IsScalarTower.left
mul_le_left
RingHom.ext

Ideal.KerLift

Theorems

NameKindAssumesProvesValidatesDepends On
map_smul 📖mathematicalDFunLike.coe
RingHom
HasQuotient.Quotient
Ideal
Ring.toSemiring
Ideal.instHasQuotient
RingHom.ker
Semiring.toNonAssocSemiring
RingHom.instFunLike
RingHom.instRingHomClass
AlgHom.toRingHom
Ideal.Quotient.ring
RingHom.instIsTwoSidedKer
RingHom.kerLift
AlgHom
AlgHom.funLike
AlgHomClass.toRingHomClass
AlgHom.algHomClass
Submodule.Quotient.instSMul'
Ring.toAddCommGroup
Semiring.toModule
Algebra.toSMul
IsScalarTower.right
AlgHomClass.toRingHomClass
AlgHom.algHomClass
RingHom.instIsTwoSidedKer
RingHom.instRingHomClass
IsScalarTower.right
Ideal.Quotient.mkₐ_surjective
map_smul
SemilinearMapClass.toMulActionSemiHomClass
NonUnitalAlgHomClass.instLinearMapClass
AlgHom.instNonUnitalAlgHomClassOfAlgHomClass

Ideal.Quotient

Definitions

NameCategoryTheorems
algebra 📖CompOp
71 mathmath: PowerSeries.IsWeierstrassFactorizationAt.algEquivQuotient_apply, Ideal.quotientEquivAlgOfEq_coe_eq_factorₐ, PowerSeries.IsWeierstrassFactorizationAt.algEquivQuotient_symm_apply, DoubleQuot.liftSupQuotQuotMkₐ_toRingHom, DoubleQuot.coe_quotQuotEquivQuotOfLEₐ_symm, DoubleQuot.coe_quotQuotMkₐ, factorₐ_comp_mk, DoubleQuot.quotQuotEquivQuotOfLEₐ_symm_toRingEquiv, DoubleQuot.quotQuotEquivComm_symmₐ, coe_factorₐ, Ideal.quotientEquivAlg_mk, Ideal.quotientEquivAlgOfEq_coe_eq_factor, factorₐ_apply_mk, AlgEquiv.quotientBot_mk, Polynomial.Monic.quotient_isIntegral, factorₐ_apply, DoubleQuot.quotQuotToQuotSupₐ_toRingHom, factorₐ_refl, Ideal.kerLiftAlg_injective, Algebra.FormallySmooth.comp_lift, mkₐ_toRingHom, KaehlerDifferential.End_equiv_aux, Algebra.FormallySmooth.exists_mkₐ_comp_eq_of_isAdicComplete, Ideal.quotientKerAlgEquivOfRightInverse_symm_apply, DoubleQuot.quotQuotEquivQuotOfLE_comp_quotQuotMkₐ, Ideal.quotientKerAlgEquivOfRightInverse_apply, DoubleQuot.coe_quotQuotEquivQuotSupₐ, Algebra.FormallyUnramified.comp_injective, Ideal.kerLiftAlg_toRingHom, DoubleQuot.coe_quotQuotEquivQuotSupₐ_symm, derivationToSquareZeroEquivLift_symm_apply_apply_coe, Ideal.quotientKerAlgEquivOfSurjective_apply, DoubleQuot.quotQuotMkₐ_toRingHom, DoubleQuot.quotQuotEquivQuotOfLE_symm_comp_mkₐ, Algebra.FormallySmooth.exists_lift, mkₐ_ker, Ideal.quotientEquivAlgOfEq_mk, Algebra.FormallySmooth.comp_surjective, Algebra.FormallyEtale.iff_comp_bijective, DoubleQuot.coe_quotQuotEquivQuotOfLEₐ, Ideal.quotientEquivAlg_symm, DoubleQuot.quotQuotEquivQuotOfLEₐ_comp_mkₐ, mkₐ_eq_mk, Ideal.quotientKerAlgEquivOfSurjective_symm_apply, Ideal.quotientKerAlgEquivOfSurjective_mk, DoubleQuot.quotQuotEquivCommₐ_toRingEquiv, DoubleQuot.coe_quotQuotToQuotSupₐ, AlgEquiv.quotientBot_symm_mk, DoubleQuot.quotQuotEquivQuotSupₐ_toRingEquiv, Ideal.quotient_map_comp_mkₐ, derivationToSquareZeroEquivLift_apply_coe_apply, Ideal.quotientMap_algebraMap, DoubleQuot.quotQuotEquivQuotOfLEₐ_toRingEquiv, Algebra.FormallyUnramified.iff_comp_injective, liftₐ_apply, DoubleQuot.quotQuotEquivComm_comp_quotQuotMkₐ, factorₐ_comp, mk_comp_algebraMap, DoubleQuot.coe_quotQuotEquivCommₐ, Ideal.quotient_map_mkₐ, Ideal.quotientEquivAlgOfEq_symm, DoubleQuot.quotQuotEquivQuotSupₐ_symm_toRingEquiv, Polynomial.IsDistinguishedAt.algEquivQuotient_apply, liftₐ_comp, mkₐ_surjective, DoubleQuot.coe_liftSupQuotQuotMkₐ, Algebra.FormallyEtale.comp_bijective, Algebra.FormallySmooth.iff_comp_surjective, Ideal.kerLiftAlg_mk, mk_algebraMap, Algebra.FormallyUnramified.iff_comp_injective_of_small
algebraQuotientOfLEComap 📖CompOp
factorₐ 📖CompOp
8 mathmath: Ideal.quotientEquivAlgOfEq_coe_eq_factorₐ, factorₐ_comp_mk, coe_factorₐ, factorₐ_apply_mk, factorₐ_apply, factorₐ_refl, DoubleQuot.quotQuotEquivQuotOfLEₐ_comp_mkₐ, factorₐ_comp
liftₐ 📖CompOp
2 mathmath: liftₐ_apply, liftₐ_comp
mkₐ 📖CompOp
46 mathmath: DoubleQuot.liftSupQuotQuotMkₐ_toRingHom, DoubleQuot.coe_quotQuotEquivQuotOfLEₐ_symm, DoubleQuot.coe_quotQuotMkₐ, factorₐ_comp_mk, DoubleQuot.quotQuotEquivQuotOfLEₐ_symm_toRingEquiv, DoubleQuot.quotQuotEquivComm_symmₐ, Polynomial.Monic.quotient_isIntegral, DoubleQuot.quotQuotToQuotSupₐ_toRingHom, Algebra.FormallySmooth.comp_lift, mkₐ_toRingHom, KaehlerDifferential.End_equiv_aux, Algebra.FormallySmooth.exists_mkₐ_comp_eq_of_isAdicComplete, DoubleQuot.quotQuotEquivQuotOfLE_comp_quotQuotMkₐ, DoubleQuot.coe_quotQuotEquivQuotSupₐ, Algebra.FormallyUnramified.comp_injective, DoubleQuot.coe_quotQuotEquivQuotSupₐ_symm, derivationToSquareZeroEquivLift_symm_apply_apply_coe, DoubleQuot.quotQuotMkₐ_toRingHom, DoubleQuot.quotQuotEquivQuotOfLE_symm_comp_mkₐ, Algebra.FormallySmooth.exists_lift, mkₐ_ker, Algebra.FormallySmooth.comp_surjective, Algebra.FormallyEtale.iff_comp_bijective, IsAdicComplete.mkₐ_comp_liftAlgHom, DoubleQuot.coe_quotQuotEquivQuotOfLEₐ, DoubleQuot.quotQuotEquivQuotOfLEₐ_comp_mkₐ, mkₐ_eq_mk, StandardEtalePresentation.toPresentation_σ', DoubleQuot.quotQuotEquivCommₐ_toRingEquiv, DoubleQuot.coe_quotQuotToQuotSupₐ, DoubleQuot.quotQuotEquivQuotSupₐ_toRingEquiv, Ideal.quotient_map_comp_mkₐ, derivationToSquareZeroEquivLift_apply_coe_apply, DoubleQuot.quotQuotEquivQuotOfLEₐ_toRingEquiv, Algebra.FormallyUnramified.iff_comp_injective, DoubleQuot.quotQuotEquivComm_comp_quotQuotMkₐ, DoubleQuot.coe_quotQuotEquivCommₐ, StandardEtalePresentation.toPresentation_relation, Ideal.quotient_map_mkₐ, DoubleQuot.quotQuotEquivQuotSupₐ_symm_toRingEquiv, liftₐ_comp, mkₐ_surjective, DoubleQuot.coe_liftSupQuotQuotMkₐ, Algebra.FormallyEtale.comp_bijective, Algebra.FormallySmooth.iff_comp_surjective, Algebra.FormallyUnramified.iff_comp_injective_of_small

Theorems

NameKindAssumesProvesValidatesDepends On
algHom_ext 📖AlgHom.comp
HasQuotient.Quotient
Ideal
Ring.toSemiring
Ideal.instHasQuotient
ring
algebra
mkₐ
AlgHom.ext
Quotient.inductionOn'
AlgHom.congr_fun
alg_map_eq 📖mathematicalalgebraMap
HasQuotient.Quotient
Ideal
CommSemiring.toSemiring
CommRing.toCommSemiring
Ideal.instHasQuotient_1
semiring
Ideal.instAlgebraQuotient
RingHom.comp
Semiring.toNonAssocSemiring
Algebra.id
algebraMap_eq 📖mathematicalalgebraMap
HasQuotient.Quotient
Ideal
CommSemiring.toSemiring
CommRing.toCommSemiring
Ideal.instHasQuotient_1
semiring
Ideal.instAlgebraQuotient
Algebra.id
CommRing.toRing
Ideal.instIsTwoSided_1
coe_factorₐ 📖mathematicalIdeal
Ring.toSemiring
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
RingHomClass.toRingHom
AlgHom
HasQuotient.Quotient
Ideal.instHasQuotient
ring
algebra
AlgHom.funLike
AlgHomClass.toRingHomClass
AlgHom.algHomClass
factorₐ
factor
AlgHomClass.toRingHomClass
AlgHom.algHomClass
factorₐ_apply 📖mathematicalIdeal
Ring.toSemiring
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
DFunLike.coe
AlgHom
HasQuotient.Quotient
Ideal.instHasQuotient
ring
algebra
AlgHom.funLike
factorₐ
RingHom
RingHom.instFunLike
factor
factorₐ_apply_mk 📖mathematicalIdeal
Ring.toSemiring
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
DFunLike.coe
AlgHom
HasQuotient.Quotient
Ideal.instHasQuotient
ring
algebra
AlgHom.funLike
factorₐ
RingHom
RingHom.instFunLike
factorₐ_comp 📖mathematicalIdeal
Ring.toSemiring
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
AlgHom.comp
HasQuotient.Quotient
Ideal.instHasQuotient
ring
algebra
factorₐ
LE.le.trans
algHom_ext
LE.le.trans
AlgHom.ext
factorₐ_comp_mk 📖mathematicalIdeal
Ring.toSemiring
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
AlgHom.comp
HasQuotient.Quotient
Ideal.instHasQuotient
ring
algebra
factorₐ
mkₐ
factorₐ_refl 📖mathematicalfactorₐ
CommRing.toCommSemiring
CommRing.toRing
Ideal.instIsTwoSided_1
le_refl
Ideal
CommSemiring.toSemiring
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
AlgHom.id
HasQuotient.Quotient
Ring.toSemiring
Ideal.instHasQuotient
ring
algebra
AlgHom.ext
Ideal.instIsTwoSided_1
le_refl
factor_eq
isScalarTower 📖mathematicalIsScalarTower
HasQuotient.Quotient
Ideal
Ring.toSemiring
Ideal.instHasQuotient
Submodule.Quotient.instSMul'
Ring.toAddCommGroup
Semiring.toModule
Algebra.toSMul
IsScalarTower.right
IsScalarTower.right
Submodule.Quotient.isScalarTower
liftₐ_apply 📖mathematicalDFunLike.coe
AlgHom
Ring.toSemiring
AlgHom.funLike
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
HasQuotient.Quotient
Ideal
Ideal.instHasQuotient
ring
algebra
liftₐ
RingHom
RingHom.instFunLike
lift
RingHomClass.toRingHom
AlgHomClass.toRingHomClass
AlgHom.algHomClass
liftₐ_comp 📖mathematicalDFunLike.coe
AlgHom
Ring.toSemiring
AlgHom.funLike
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
AlgHom.comp
HasQuotient.Quotient
Ideal
Ideal.instHasQuotient
ring
algebra
liftₐ
mkₐ
AlgHom.ext
AlgHomClass.toRingHomClass
AlgHom.algHomClass
mk_algebraMap 📖mathematicalDFunLike.coe
RingHom
HasQuotient.Quotient
Ideal
Ring.toSemiring
Ideal.instHasQuotient
Semiring.toNonAssocSemiring
ring
RingHom.instFunLike
CommSemiring.toSemiring
algebraMap
algebra
mk_bijective_iff_eq_bot 📖mathematicalFunction.Bijective
HasQuotient.Quotient
Ideal
Ring.toSemiring
Ideal.instHasQuotient
DFunLike.coe
RingHom
Semiring.toNonAssocSemiring
ring
RingHom.instFunLike
Bot.bot
Submodule.instBot
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toModule
Ideal.map_eq_bot_iff_of_injective
RingHom.instRingHomClass
Ideal.map_eq_bot_iff_le_ker
le_of_eq
Ideal.mk_ker
RingHom.injective_iff_ker_eq_bot
mk_surjective
mk_comp_algebraMap 📖mathematicalRingHom.comp
HasQuotient.Quotient
Ideal
Ring.toSemiring
Ideal.instHasQuotient
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
ring
algebraMap
algebra
mkₐ_eq_mk 📖mathematicalDFunLike.coe
AlgHom
HasQuotient.Quotient
Ideal
Ring.toSemiring
Ideal.instHasQuotient
ring
algebra
AlgHom.funLike
mkₐ
RingHom
Semiring.toNonAssocSemiring
RingHom.instFunLike
mkₐ_ker 📖mathematicalRingHom.ker
HasQuotient.Quotient
Ideal
Ring.toSemiring
Ideal.instHasQuotient
RingHom
Semiring.toNonAssocSemiring
ring
RingHom.instFunLike
RingHom.instRingHomClass
RingHomClass.toRingHom
AlgHom
algebra
AlgHom.funLike
AlgHomClass.toRingHomClass
AlgHom.algHomClass
mkₐ
Ideal.mk_ker
mkₐ_surjective 📖mathematicalHasQuotient.Quotient
Ideal
Ring.toSemiring
Ideal.instHasQuotient
DFunLike.coe
AlgHom
ring
algebra
AlgHom.funLike
mkₐ
Quot.mk_surjective
mkₐ_toRingHom 📖mathematicalAlgHom.toRingHom
HasQuotient.Quotient
Ideal
Ring.toSemiring
Ideal.instHasQuotient
ring
algebra
mkₐ
smul_top 📖mathematicalSubmodule
HasQuotient.Quotient
Ideal
CommSemiring.toSemiring
CommRing.toCommSemiring
Ideal.instHasQuotient_1
NonUnitalNonAssocSemiring.toAddCommMonoid
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
commRing
Submodule.Quotient.module
CommRing.toRing
Ring.toAddCommGroup
Semiring.toModule
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddMonoidWithOne.toAddMonoid
AddCommMonoidWithOne.toAddMonoidWithOne
Submodule.instAddCommMonoidWithOne
semiring
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Submodule.pointwiseDistribMulAction
Submodule.Quotient.distribMulAction
Submodule.Quotient.smulCommClass
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
instDistribSMul
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
SemigroupAction.toSMul
Monoid.toSemigroup
Ring.toSemiring
MulAction.toSemigroupAction
DistribMulAction.toMulAction
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
Module.toDistribMulAction
AddCommGroup.toAddCommMonoid
Algebra.to_smulCommClass
Algebra.id
Top.top
Submodule.instTop
Submodule.span
Submodule.hasQuotient
Set
Set.instSingletonSet
Submodule.Quotient.smulCommClass
Algebra.to_smulCommClass
Ideal.instIsTwoSided_1
Submodule.smul_span
Set.smul_set_singleton
Algebra.smul_def
mul_one
span_singleton_one 📖mathematicalSubmodule.span
HasQuotient.Quotient
Ideal
Ring.toSemiring
Ideal.instHasQuotient
NonUnitalNonAssocSemiring.toAddCommMonoid
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
ring
Submodule.Quotient.module
Ring.toAddCommGroup
Semiring.toModule
Set
Set.instSingletonSet
one
Top.top
Submodule
Submodule.instTop
map_one
MonoidHomClass.toOneHomClass
MonoidWithZeroHomClass.toMonoidHomClass
RingHomClass.toMonoidWithZeroHomClass
RingHom.instRingHomClass
RingHomSurjective.ids
Submodule.range_mkQ
Submodule.map_top
Ideal.span_singleton_one
Ideal.span.eq_1
Submodule.map_span
Set.image_singleton
Submodule.mkQ_apply

RingEquiv

Definitions

NameCategoryTheorems
quotientBot 📖CompOp
2 mathmath: quotientBot_symm_mk, quotientBot_mk

Theorems

NameKindAssumesProvesValidatesDepends On
quotientBot_mk 📖mathematicalDFunLike.coe
RingEquiv
HasQuotient.Quotient
Ideal
Ring.toSemiring
Ideal.instHasQuotient
Bot.bot
Submodule.instBot
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
Ideal.Quotient.ring
Ideal.instIsTwoSidedBot
Distrib.toAdd
EquivLike.toFunLike
instEquivLike
quotientBot
RingHom
RingHom.instFunLike
Ideal.instIsTwoSidedBot
quotientBot_symm_mk 📖mathematicalDFunLike.coe
RingEquiv
HasQuotient.Quotient
Ideal
Ring.toSemiring
Ideal.instHasQuotient
Bot.bot
Submodule.instBot
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
Ideal.Quotient.ring
Ideal.instIsTwoSidedBot
Distrib.toAdd
EquivLike.toFunLike
instEquivLike
symm
quotientBot
RingHom
RingHom.instFunLike
Ideal.instIsTwoSidedBot

RingHom

Definitions

NameCategoryTheorems
kerLift 📖CompOp
7 mathmath: Ideal.quotientKerAlgEquivOfRightInverse_apply, Ideal.kerLiftAlg_toRingHom, Ideal.quotientKerAlgEquivOfSurjective_apply, kerLift_injective, quotientKerEquivOfRightInverse.apply, Ideal.KerLift.map_smul, kerLift_mk
quotientKerEquivOfRightInverse 📖CompOp
2 mathmath: quotientKerEquivOfRightInverse.Symm.apply, quotientKerEquivOfRightInverse.apply
quotientKerEquivOfSurjective 📖CompOp
3 mathmath: quotientKerEquivOfSurjective_symm_apply, quotientKerEquivOfSurjective_symm_comp, quotientKerEquivOfSurjective_apply_mk
quotientKerEquivRange 📖CompOp
quotientKerEquivRangeS 📖CompOp

Theorems

NameKindAssumesProvesValidatesDepends On
kerLift_injective 📖mathematicalHasQuotient.Quotient
Ideal
Ring.toSemiring
Ideal.instHasQuotient
ker
RingHom
Semiring.toNonAssocSemiring
instFunLike
instRingHomClass
DFunLike.coe
Ideal.Quotient.ring
instIsTwoSidedKer
kerLift
lift_injective_of_ker_le_ideal
instRingHomClass
instIsTwoSidedKer
le_rfl
kerLift_mk 📖mathematicalDFunLike.coe
RingHom
HasQuotient.Quotient
Ideal
Ring.toSemiring
Ideal.instHasQuotient
ker
Semiring.toNonAssocSemiring
instFunLike
instRingHomClass
Ideal.Quotient.ring
instIsTwoSidedKer
kerLift
lift_injective_of_ker_le_ideal 📖mathematicalDFunLike.coe
RingHom
Semiring.toNonAssocSemiring
Ring.toSemiring
instFunLike
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonAssocSemiring.toNonUnitalNonAssocSemiring
Ideal
Preorder.toLE
PartialOrder.toPreorder
Submodule.instPartialOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
Semiring.toModule
ker
instRingHomClass
HasQuotient.Quotient
Ideal.instHasQuotient
Ideal.Quotient.ring
Ideal.Quotient.lift
instRingHomClass
injective_iff_ker_eq_bot
ker_eq_bot_iff_eq_zero
Ideal.Quotient.mk_surjective
Ideal.Quotient.eq_zero_iff_mem
mem_ker
quotientKerEquivOfSurjective_apply_mk 📖mathematicalDFunLike.coe
RingHom
Semiring.toNonAssocSemiring
Ring.toSemiring
instFunLike
RingEquiv
HasQuotient.Quotient
Ideal
Ideal.instHasQuotient
ker
instRingHomClass
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
Ideal.Quotient.ring
instIsTwoSidedKer
NonAssocSemiring.toNonUnitalNonAssocSemiring
Distrib.toAdd
EquivLike.toFunLike
RingEquiv.instEquivLike
quotientKerEquivOfSurjective
instRingHomClass
instIsTwoSidedKer
quotientKerEquivOfSurjective_symm_apply 📖mathematicalDFunLike.coe
RingHom
Semiring.toNonAssocSemiring
Ring.toSemiring
instFunLike
RingEquiv
HasQuotient.Quotient
Ideal
Ideal.instHasQuotient
ker
instRingHomClass
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
Ideal.Quotient.ring
instIsTwoSidedKer
Distrib.toAdd
EquivLike.toFunLike
RingEquiv.instEquivLike
RingEquiv.symm
quotientKerEquivOfSurjective
RingEquiv.injective
instRingHomClass
instIsTwoSidedKer
RingEquiv.apply_symm_apply
quotientKerEquivOfSurjective_symm_comp 📖mathematicalDFunLike.coe
RingHom
Semiring.toNonAssocSemiring
Ring.toSemiring
instFunLike
comp
HasQuotient.Quotient
Ideal
Ideal.instHasQuotient
ker
instRingHomClass
Ideal.Quotient.ring
instIsTwoSidedKer
RingEquiv.toRingHom
RingEquiv.symm
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
NonAssocSemiring.toNonUnitalNonAssocSemiring
Distrib.toAdd
quotientKerEquivOfSurjective
ext
instRingHomClass
instIsTwoSidedKer
quotientKerEquivOfSurjective_symm_apply

RingHom.quotientKerEquivOfRightInverse

Theorems

NameKindAssumesProvesValidatesDepends On
apply 📖mathematicalDFunLike.coe
RingHom
Semiring.toNonAssocSemiring
Ring.toSemiring
RingHom.instFunLike
RingEquiv
HasQuotient.Quotient
Ideal
Ideal.instHasQuotient
RingHom.ker
RingHom.instRingHomClass
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
Ideal.Quotient.ring
RingHom.instIsTwoSidedKer
NonAssocSemiring.toNonUnitalNonAssocSemiring
Distrib.toAdd
EquivLike.toFunLike
RingEquiv.instEquivLike
RingHom.quotientKerEquivOfRightInverse
RingHom.kerLift
RingHom.instRingHomClass
RingHom.instIsTwoSidedKer

RingHom.quotientKerEquivOfRightInverse.Symm

Theorems

NameKindAssumesProvesValidatesDepends On
apply 📖mathematicalDFunLike.coe
RingHom
Semiring.toNonAssocSemiring
Ring.toSemiring
RingHom.instFunLike
RingEquiv
HasQuotient.Quotient
Ideal
Ideal.instHasQuotient
RingHom.ker
RingHom.instRingHomClass
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
Ideal.Quotient.ring
RingHom.instIsTwoSidedKer
Distrib.toAdd
EquivLike.toFunLike
RingEquiv.instEquivLike
RingEquiv.symm
RingHom.quotientKerEquivOfRightInverse
RingHom.instRingHomClass
RingHom.instIsTwoSidedKer

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