instHasQuotient 📖 | CompOp | 399 mathmath: PowerSeries.IsWeierstrassFactorizationAt.algEquivQuotient_apply, quotientEquivAlgOfEq_coe_eq_factorₐ, Quotient.isScalarTower, IsLocalization.surjective_quotientMap_of_maximal_of_localization, PowerSeries.IsWeierstrassFactorizationAt.algEquivQuotient_symm_apply, DoubleQuot.liftSupQuotQuotMkₐ_toRingHom, Int.quotientSpanEquivZMod_comp_Quotient_mk, StandardEtalePair.inv_aeval_X_g, IsLocalization.AtPrime.equivQuotientMapOfIsMaximal_apply_mk, RingTheory.Sequence.isWeaklyRegular_cons_iff', quotientEquiv_symm_apply, AdjoinRoot.quotMapOfEquivQuotMapCMapSpanMk_symm_mk, algebraMap_quotient_injective, DoubleQuot.coe_quotQuotEquivQuotOfLEₐ_symm, Ring.coe_jacobson_quotient, Polynomial.fiberEquivQuotient_tmul, quotientMap_comp_mk, RingHom.quotientKerEquivOfSurjective_symm_apply, Quotient.factor_comp_mk, comap_cotangentIdeal, DoubleQuot.coe_quotQuotMkₐ, Quotient.factorₐ_comp_mk, Int.quotientSpanNatEquivZMod_comp_Quotient_mk, StandardEtalePresentation.toPresentation_algebra_smul, quotient_map_C_eq_zero, Polynomial.IsDistinguishedAt.map_eq_X_pow, AlgHom.IsArithFrobAt.mk_apply, map_mk_comap_factor, WittVector.factorPowSucc_comp_fontaineThetaModPPow, PowerBasis.quotientEquivQuotientMinpolyMap_apply, quotientInfToPiQuotient_inj, torsionMapQuot_apply, Quotient.algEquivOfEqMap_apply, Quotient.factor_mk, algebraMap_quotient_residueField_mk, quotientInfToPiQuotient_surj, AlgEquiv.prodQuotientOfIsIdempotentElem_apply, DoubleQuot.quotQuotEquivQuotOfLEₐ_symm_toRingEquiv, Algebra.Generators.compLocalizationAwayAlgHom_toAlgHom_toComp, height_eq_height_add_of_liesOver_of_hasGoingDown, DoubleQuot.quotQuotEquivComm_symmₐ, Quotient.subsingleton_iff, WittVector.factorPowSucc_fontaineThetaModPPow_eq, Quotient.coe_factorₐ, Quotient.factor_comp_apply, quotientEquivAlg_mk, Ring.jacobson_quotient_of_le, quotientEquivAlgOfEq_coe_eq_factor, RingHom.quotientKerEquivOfSurjective_symm_comp, Quotient.factorₐ_apply_mk, Polynomial.IsDistinguishedAt.degree_eq_coe_lift_order_map, Quotient.instIsPrimeQuotientMapRingHomAlgebraMapMkOfLiesOver, AdjoinRoot.quotEquivQuotMap_symm_apply_mk, IsLocalRing.basisQuotient_repr, Quotient.algebraMap_quotient_of_ramificationIdx_neZero, AlgEquiv.quotientBot_mk, RingEquiv.quotientBot_symm_mk, quotEquivOfEq_mk, injective_quotient_le_comap_map, Quotient.algebraMap_quotient_map_quotient, PreTilt.mk_comp_untilt_eq_coeff_zero, DoubleQuot.quotQuotEquivComm_comp_quotQuotMk, Algebra.PreSubmersivePresentation.ofHasCoeffs_σ', Algebra.Presentation.quotientEquiv_symm, DoubleQuot.quotQuotEquivComm_quotQuotMk, Polynomial.Monic.quotient_isIntegral, Quotient.exists_inv, WittVector.mk_pow_fontaineTheta, ker_Pi_Quotient_mk, Algebra.Generators.naive_val, Quotient.factorₐ_apply, powQuotSuccInclusion_apply_coe, PowerBasis.quotientEquivQuotientMinpolyMap_apply_mk, Module.IsTorsionBySet.mk_smul, DoubleQuot.quotQuotToQuotSupₐ_toRingHom, Algebra.Generators.compLocalizationAwayAlgHom_X_inl, Quotient.lift_surjective_of_surjective, AddValuation.self_le_supp_comap, Submodule.factor_eq_factor, PrimeSpectrum.comap_quotientMk_bijective_of_le_nilradical, Quotient.factorₐ_refl, IsLocalization.AtPrime.equivQuotientMapOfIsMaximal_symm_apply_mk, kerLiftAlg_injective, Polynomial.modByMonic_eq_zero_iff_quotient_eq_zero, AddValuation.onQuot_comap_eq, AdicCompletion.mkₐ_apply_coe, StandardEtalePair.equivMvPolynomialQuotient_symm_apply, map_mk_comap_factorPow, Quotient.span_singleton_one, PowerSeries.IsWeierstrassDivisionAt.degree_lt, PowerBasis.quotientEquivQuotientMinpolyMap_symm_apply_mk, map_mk_eq_bot_of_le, IsLocalRing.residue_def, Polynomial.Monic.quotient_isIntegralElem, PowerSeries.IsWeierstrassFactorizationAt.natDegree_eq_toNat_order_map_of_ne_top, Algebra.FormallySmooth.comp_lift, RingQuot.idealQuotientToRingQuot_apply, height_le_height_add_of_liesOver, height_le_height_add_one_of_mem, Quotient.mkₐ_toRingHom, RingEquiv.quotientBot_mk, KaehlerDifferential.End_equiv_aux, Algebra.PreSubmersivePresentation.ofHasCoeffs_algebra_algebraMap_apply, MvPolynomial.quotient_map_C_eq_zero, AdjoinRoot.quotMapCMapSpanMkEquivQuotMapCQuotMapSpanMk_symm_quotQuotMk, comp_quotientMap_eq_of_comp_eq, Quotient.eq_zero_iff_dvd, Module.Quotient.mk_smul_mk, Algebra.FormallySmooth.exists_mkₐ_comp_eq_of_isAdicComplete, liftOfDerivationToSquareZero_mk_apply, Quotient.isDomain_iff_prime, quotientEquiv_symm_mk, isStronglyTranscendental_mk_radical_conductor, Quotient.nontrivial_iff, Quotient.mk_singleton_self, IsLocalization.Away.mvPolynomialQuotientEquiv_apply, quotientToQuotientRangePowQuotSucc_mk, AdjoinRoot.quotEquivQuotMap_apply, quotientKerAlgEquivOfRightInverse_symm_apply, PowerSeries.IsWeierstrassDivisorAt.mod'_mk_eq_mod, Valuation.comap_onQuot_eq, Algebra.Generators.sq_ker_comp_le_ker_compLocalizationAwayAlgHom, DoubleQuot.quotQuotEquivQuotOfLE_comp_quotQuotMkₐ, Quotient.mk_bijective_iff_eq_bot, KummerDedekind.emultiplicity_factors_map_eq_emultiplicity, Algebra.FormallySmooth.mk_lift, RingHom.lift_injective_of_ker_le_ideal, mem_quotient_iff_mem, QuotientRing.isOpenMap_coe, AdicCompletion.factorₐ_evalₐ_one, TensorProduct.tensorQuotEquivQuotSMul_tmul_mk, QuotientRing.isQuotientMap_coe_coe, quotientKerAlgEquivOfRightInverse_apply, Quotient.mk_span_range, Polynomial.quotientSpanXSubCAlgEquiv_mk, DoubleQuot.ker_quotQuotMk, AdicCompletion.mk_ofAlgEquiv_symm, AdicCompletion.mk_smul_mk, DoubleQuot.coe_quotQuotEquivQuotSupₐ, quotientMulEquivQuotientProd_snd, isPrime_map_quotientMk_of_isPrime, algebraMap_mk, Quotient.stabilizerHom_apply, AlgebraicGeometry.IsClosedImmersion.spec_of_quotient_mk, Quotient.torsionBy_eq_span_singleton, RingHom.pi_bijective_of_isIdempotentElem, ModP.preVal_mk, Quotient.nontrivial, map_quotient_self, tensorKaehlerQuotKerSqEquiv_symm_tmul_D, AlgebraicGeometry.Scheme.IdealSheafData.subschemeι_app, finite_iff_ideal_quotient, mk_mem_cotangentIdeal, Int.quotientSpanEquivZMod_comp_castRingHom, quotientMap_mk, quotAdjoinEquivQuotMap_apply_mk, Quotient.lift_mk, quotientToQuotientRangePowQuotSucc_surjective, WittVector.ker_map_le_ker_mk_comp_ghostComponent, Algebra.FormallyUnramified.comp_injective, WittVector.fontaineThetaModPPow_teichmuller, Quotient.factor_surjective, PowerSeries.IsWeierstrassDivisorAt.isUnit_shift, RingTheory.Sequence.isWeaklyRegular_append_iff', Valuation.supp_quot, kerLiftAlg_toRingHom, DoubleQuot.coe_quotQuotEquivQuotSupₐ_symm, OrthogonalIdempotents.surjective_pi, Quotient.eq_zero_iff_mem, tensorKaehlerQuotKerSqEquiv_tmul_D, derivationToSquareZeroEquivLift_symm_apply_apply_coe, WittVector.ghostComponentModPPow_teichmuller_coeff, Quotient.algEquivOfEqComap_apply, quotEquivOfEq_eq_factor, quotientKerAlgEquivOfSurjective_apply, DoubleQuot.quotQuotMkₐ_toRingHom, ker_quotient_lift, Polynomial.quotient_mk_comp_C_isIntegral_of_isJacobsonRing, Quotient.algebraMap_quotient_pow_ramificationIdx, RingHom.prod_bijective_of_isIdempotentElem, DoubleQuot.quotQuotEquivQuotOfLE_symm_comp_mkₐ, RingHom.quotientKerEquivOfRightInverse.Symm.apply, IsLocalization.AtPrime.equivQuotMaximalIdeal_apply_mk, AdicCompletion.Ideal.mk_eq_mk, AdjoinRoot.quotEquivQuotMap_apply_mk, PowerBasis.quotientEquivQuotientMinpolyMap_symm_apply, comap_map_quotientMk, Algebra.FormallySmooth.exists_lift, Algebra.Presentation.tensorModelOfHasCoeffsEquiv_tmul, minimalPrimes_eq_comap, Submodule.torsionBy.mk_ideal_smul, Quotient.mkₐ_ker, Quotient.mk_surjective, Quotient.eq, quotientEquivAlgOfEq_mk, RingHom.quotientKerEquivOfSurjective_apply_mk, Algebra.Presentation.tensorModelOfHasCoeffsHom_tmul, injective_lift_iff, Quotient.factor_ker, AlgebraicGeometry.Scheme.IdealSheafData.isLocalization_away, DoubleQuot.ker_quotLeftToQuotSup, Algebra.FormallySmooth.comp_surjective, Algebra.FormallyEtale.iff_comp_bijective, quotientEquiv_apply, AdjoinRoot.Polynomial.quotQuotEquivComm_mk, quotientInfEquivQuotientProd_snd, MvPolynomial.quotient_mk_comp_C_isIntegral_of_isJacobsonRing, Ring.DirectLimit.quotientMk_of, IsSemiprimaryRing.isSemisimpleRing, comap_map_mk, DoubleQuot.coe_quotQuotEquivQuotOfLEₐ, quotientToQuotientRangePowQuotSucc_injective, Quotient.ringHom_ext_iff, RingOfIntegers.ZModXQuotSpanEquivQuotSpan_mk_apply, RingHom.kerLift_injective, Quotient.isDomain, MvPolynomial.quotientEquivQuotientMvPolynomial_leftInverse, AdicCompletion.evalOneₐ_of, Quotient.mk_out, instIsArtinianRingQuotientIdeal, Algebra.trace_quotient_mk, polynomialQuotientEquivQuotientPolynomial_symm_mk, Polynomial.IsDistinguishedAt.algEquivQuotient_symm_apply, MvPolynomial.quotient_mk_comp_C_injective, AlgebraicClosure.Monics.map_eq_prod, AdicCompletion.mk_smul_top_ofAlgEquiv_symm, quotientMap_injective', quotientEquivAlg_symm, Algebra.TensorProduct.quotIdealMapEquivTensorQuot_symm_tmul, RingHom.IsIntegral.quotient, IsLocalRing.quotient_span_eq_top_iff_span_eq_top, DividedPowers.Quotient.isDPMorphism, quotientMulEquivQuotientProd_fst, DoubleQuot.quotQuotEquivQuotOfLEₐ_comp_mkₐ, rank_pow_quot_aux, Quotient.mkₐ_eq_mk, rootsOfUnityMapQuot_apply, StandardEtalePresentation.toPresentation_σ', Module.IsTorsionBySet.isScalarTower, AlgEquiv.prodQuotientOfIsIdempotentElem_apply_snd, rank_pow_quot, AdicCompletion.mk_ofAlgEquiv_symm_eq_evalOneₐ, map_height_le_one_of_mem_minimalPrimes, AdjoinRoot.quotAdjoinRootEquivQuotPolynomialQuot_symm_mk_mk, DoubleQuot.quotQuotEquivQuotSup_quotQuotMk, Module.IsTorsionBySet.isSemisimpleModule_iff, quotientKerAlgEquivOfSurjective_symm_apply, quotientKerAlgEquivOfSurjective_mk, mem_quotient_iff_mem_sup, DoubleQuot.quotQuotEquivCommₐ_toRingEquiv, DoubleQuot.coe_quotQuotToQuotSupₐ, Quotient.norm_mk_lt, Valuation.onQuot_comap_eq, AlgEquiv.quotientBot_symm_mk, IsLocalRing.basisQuotient_apply, trace_quotient_eq_trace_localization_quotient, Quotient.mk_eq_mk_iff_sub_mem, quotientEquiv_mk, quotientMap_surjective, ker_quotientMap_mk, AdjoinRoot.Polynomial.quotQuotEquivComm_symm_mk_mk, powQuotSuccInclusion_injective, DoubleQuot.quotQuotEquivQuotSupₐ_toRingEquiv, Algebra.trace_quotient_eq_of_isDedekindDomain, quotient_map_comp_mkₐ, StandardEtalePair.aeval_X_g_mul_mk_X, AdicCompletion.transitionMap_ideal_mk, Algebra.Presentation.tensorModelOfHasCoeffsEquiv_symm_tmul, Quotient.smulCommClass', quotientInfToPiQuotient_mk', AlgEquiv.prodQuotientOfIsIdempotentElem_apply_fst, Quotient.mk_eq_mk, quotEquivOfEq_symm, Quotient.instRingHomSurjectiveQuotientMk, Algebra.TensorProduct.quotIdealMapEquivTensorQuot_mk, PrimeSpectrum.range_comap_algebraMap_localization_compl_eq_range_comap_quotientMk, StandardEtalePresentation.toPresentation_algebra_algebraMap_apply, isLocalHom_of_le_jacobson_bot, quotientInfToPiQuotient_mk, derivationToSquareZeroEquivLift_apply_coe_apply, AdjoinRoot.quotMapOfEquivQuotMapCMapSpanMk_mk, liftOfDerivationToSquareZero_mk_apply', quotientInfEquivQuotientProd_fst, univ_eq_iUnion_image_add, PowerSeries.IsWeierstrassFactorizationAt.degree_eq_coe_lift_order_map_of_ne_top, quotientMap_algebraMap, DoubleQuot.quotQuotEquivQuotOfLEₐ_toRingEquiv, Algebra.FormallyUnramified.iff_comp_injective, WittVector.quotEquivOfEq_ghostComponentModPPow, AdicCompletion.evalₐ_of, AdjoinRoot.quotEquivQuotMap_symm_apply, CompleteOrthogonalIdempotents.bijective_pi', PowerSeries.isWeierstrassDivisionAt_iff, StandardEtalePresentation.toPresentation_val, height_le_height_add_encard_of_subset, DividedPowers.Quotient.dpow_apply, Algebra.Generators.compLocalizationAwayAlgHom_relation_eq_zero, Quotient.mk_eq_one_iff_sub_mem, AdjoinRoot.quotMapCMapSpanMkEquivQuotMapCQuotMapSpanMk_mk, quotientMap_injective, KummerDedekind.normalizedFactors_ideal_map_eq_normalizedFactors_min_poly_mk_map, AdicCompletion.factor_evalₐ_eq_eval, isStronglyTranscendental_mk_of_mem_minimalPrimes, cotangentEquivIdeal_symm_apply, Quotient.smulCommClass, RingHom.quotientKerEquivOfRightInverse.apply, Quotient.liftₐ_apply, MvPolynomial.eval₂_C_mk_eq_zero, Quotient.instNonemptyQuotient, PowerSeries.IsWeierstrassDivisorAt.mk_mod'_eq_self, idealFactorsFunOfQuotHom_coe_coe, AdicCompletion.evalₐ_mk, DoubleQuot.quotQuotEquivComm_comp_quotQuotMkₐ, KerLift.map_smul, IsLocalization.AtPrime.equivQuotientMapMaximalIdeal_apply_mk, DoubleQuot.quotQuotEquivComm_mk_mk, AlgHom.IsArithFrobAt.restrict_mk, AdicCompletion.evalₐ_mkₐ, Algebra.Presentation.quotientEquiv_mk, isSemiprimaryRing_iff, DoubleQuot.quotQuotEquivQuotOfLE_symm_comp_mk, Quotient.quotient_ring_saturate, DoubleQuot.quotQuotEquivQuotSup_symm_quotQuotMk, Quotient.factorₐ_comp, Valuation.self_le_supp_comap, mk_ker, height_le_height_add_spanFinrank_of_le, Submodule.torsionBySet.mk_smul, Quotient.factor_comp, Quotient.mk_comp_algebraMap, DoubleQuot.coe_quotQuotEquivCommₐ, Algebra.PreSubmersivePresentation.ofHasCoeffs_val, polynomialQuotientEquivQuotientPolynomial_map_mk, IsDedekindDomain.exists_representative_mod_finset, AlgebraicGeometry.Scheme.IdealSheafData.glueDataObjι_ι, MvPolynomial.quotientEquivQuotientMvPolynomial_rightInverse, DoubleQuot.quotQuotEquivQuotSup_quot_quot_algebraMap, IsLocalization.AtPrime.equivQuotMaximalIdeal_symm_apply_mk, quotient_mk_maps_eq, DoubleQuot.quotQuotEquivQuotOfLE_symm_mk, isIntegral_quotientMap_iff, AddValuation.comap_onQuot_eq, Quotient.lift_comp_mk, PreTilt.mk_untilt_eq_coeff_zero, AlgHom.kerSquareLift_mk, Quotient.factor_eq, WittVector.mk_fontaineTheta, IsNilpotent.isUnit_quotient_mk_iff, Quotient.norm_mk_le, quotTorsionOfEquivSpanSingleton_apply_mk, quotientToQuotientRangePowQuotSuccAux_mk, PowerSeries.IsWeierstrassDivisorAt.seq_one, bot_quotient_isMaximal_iff, Factors.piQuotientEquiv_mk, quotient_map_mkₐ, RingHom.kerLift_mk, QuotientRing.isOpenQuotientMap_mk, quotientEquivAlgOfEq_symm, DoubleQuot.quotQuotEquivQuotSupₐ_symm_toRingEquiv, Quotient.isScalarTower_right, Polynomial.IsDistinguishedAt.algEquivQuotient_apply, eval₂_C_mk_eq_zero, Quotient.liftₐ_comp, Quotient.mk_smul_mk_quotient_map_quotient, AddValuation.supp_quot, Quotient.mkₐ_surjective, IsDedekindDomain.quotientEquivPiFactors_mk, AdjoinRoot.quotAdjoinRootEquivQuotPolynomialQuot_mk_of, Ring.jacobson_quotient_jacobson, Module.IsTorsionBy.mk_smul, RingTheory.Sequence.isRegular_cons_iff', ValuationSubring.coe_unitGroupToResidueFieldUnits_apply, Quotient.zero_eq_one_iff, DoubleQuot.coe_liftSupQuotQuotMkₐ, NumberField.Ideal.primesOverSpanEquivMonicFactorsMod_symm_apply, DoubleQuot.quotQuotEquivQuotOfLE_comp_quotQuotMk, Algebra.FormallyEtale.comp_bijective, Int.quotientSpanNatEquivZMod_comp_castRingHom, Submodule.torsionBy.mk_smul, WittVector.ghostComponentModPPow_map_mk, Algebra.FormallySmooth.iff_comp_surjective, Polynomial.IsDistinguishedAt.coe_natDegree_eq_order_map, kerLiftAlg_mk, pi_quotient_surjective, DoubleQuot.quotQuotEquivQuotOfLE_quotQuotMk, CompleteOrthogonalIdempotents.bijective_pi, DoubleQuot.quotQuotEquivComm_symm, Factors.piQuotientEquiv_map, TensorProduct.quotTensorEquivQuotSMul_mk_tmul, derivationQuotKerSq_mk, Quotient.noZeroDivisors, DoubleQuot.quotQuotEquivComm_algebraMap, Quotient.mk_algebraMap, Algebra.FormallyUnramified.iff_comp_injective_of_small, Polynomial.isIntegral_isLocalization_polynomial_quotient, Quotient.algebraMap_mk_of_liesOver, RingQuot.ringQuotToIdealQuotient_apply, Algebra.Presentation.tensorModelOfHasCoeffsInv_aeval_val, KummerDedekind.quotMapEquivQuotQuotMap_symm_apply
|
instHasQuotient_1 📖 | CompOp | 368 mathmath: PowerSeries.IsWeierstrassFactorizationAt.algEquivQuotient_apply, toCotangent_to_quotient_square, Quotient.nontrivial_of_liesOver_of_isPrime, Submodule.instIsScalarTowerQuotientIdealSubtypeMemTorsionBySetCoe, Quotient.exists_algHom_fixedPoint_quotient_under, PowerSeries.IsWeierstrassFactorizationAt.algEquivQuotient_symm_apply, Algebra.PreSubmersivePresentation.jacobiMatrix_naive, Algebra.FiniteType.quotient, DoubleQuot.liftSupQuotQuotMkₐ_toRingHom, ringKrullDim_quotient_span_singleton_succ_eq_ringKrullDim, Quotient.map_ker_stabilizer_subtype, Valuation.supp_quot_supp, IsAdicComplete.StrictMono.mk_liftRingHom, Int.quotientSpanEquivZMod_comp_Quotient_mk, Polynomial.Monic.free_quotient, Algebra.Presentation.naive_toGenerators, IsLocalization.AtPrime.equivQuotientMapOfIsMaximal_apply_mk, AdicCompletion.map_val_apply, AdjoinRoot.quotMapOfEquivQuotMapCMapSpanMk_symm_mk, rank_prime_pow_ramificationIdx, algebraMap_quotient_injective, finrank_quotient_span_eq_natDegree_norm, DoubleQuot.coe_quotQuotEquivQuotOfLEₐ_symm, Polynomial.fiberEquivQuotient_tmul, comap_cotangentIdeal, Polynomial.quotientSpanXSubCAlgEquiv_symm_apply, QuotSMulTop.equivTensorQuot_naturality, DoubleQuot.coe_quotQuotMkₐ, Int.quotientSpanNatEquivZMod_comp_Quotient_mk, IsLocalRing.finrank_quotient_map, StandardEtalePresentation.toPresentation_algebra_smul, Module.supportDim_eq_ringKrullDim_quotient_annihilator, AlgHom.IsArithFrobAt.mk_apply, PowerBasis.quotientEquivQuotientMinpolyMap_apply, DoubleQuot.coe_quotLeftToQuotSupₐ, AdicCompletion.val_smul_eq_evalₐ_smul, inertiaDeg_algebraMap, torsionMapQuot_apply, Quotient.algEquivOfEqMap_apply, range_cotangentToQuotientSquare, Algebra.QuasiFinite.instQuotientIdeal, algebraMap_quotient_residueField_mk, instIsSeparableQuotientIdealOfResidueField, instFiniteQuotientRingOfIntegersIdealOfNumberFieldOfIsMaximal, finrank_quotient_span_eq_natDegree', Quotient.instFaithfulSMul, Module.exists_smul_eq_zero_and_mk_eq, TensorProduct.quotTensorEquivQuotSMul_comp_mkQ_rTensor, QuotientMapQuotient.isNoetherian, AlgEquiv.prodQuotientOfIsIdempotentElem_apply, DoubleQuot.quotQuotEquivQuotOfLEₐ_symm_toRingEquiv, Quotient.tower_quotient_map_quotient, DoubleQuot.quotQuotEquivComm_symmₐ, ringKrullDim_quotient, WittVector.factorPowSucc_fontaineThetaModPPow_eq, QuotSMulTop.equivTensorQuot_naturality_mk, Module.equiv_directSum_of_isTorsion, TensorProduct.tensorQuotEquivQuotSMul_comp_mkQ_lTensor, rootsOfUnityMapQuot_injective, AdjoinRoot.quotEquivQuotMap_symm_apply_mk, algebra_finiteType_of_liesOver, IsLocalRing.basisQuotient_repr, Quotient.algebraMap_quotient_of_ramificationIdx_neZero, AdicCompletion.pi_apply_coe, Quotient.stabilizerHom_surjective, Quotient.algebraMap_eq, Quotient.algebraMap_quotient_map_quotient, DoubleQuot.quotQuotEquivComm_comp_quotQuotMk, Algebra.PreSubmersivePresentation.ofHasCoeffs_σ', DoubleQuot.quotQuotEquivComm_quotQuotMk, WittVector.mk_pow_fontaineTheta, AdicCompletion.factor_eval_eq_evalₐ, Algebra.Generators.naive_val, powQuotSuccInclusion_apply_coe, PowerBasis.quotientEquivQuotientMinpolyMap_apply_mk, DoubleQuot.quotQuotToQuotSupₐ_toRingHom, AlgebraicGeometry.Scheme.Hom.liftQuotient_comp, Algebra.Presentation.naive_relation, IsLocalization.AtPrime.equivQuotientMapOfIsMaximal_symm_apply_mk, IsLocalization.AtPrime.exists_algebraMap_quot_eq_of_mem_quot, Algebra.FormallyUnramified.isField_quotient_map_maximalIdeal, StandardEtalePair.equivMvPolynomialQuotient_symm_apply, normalizedFactorsEquivOfQuotEquiv_symm, PowerBasis.quotientEquivQuotientMinpolyMap_symm_apply_mk, RingQuot.idealQuotientToRingQuot_apply, KaehlerDifferential.End_equiv_aux, finrank_quotient_span_eq_natDegree, Algebra.PreSubmersivePresentation.ofHasCoeffs_algebra_algebraMap_apply, AdjoinRoot.quotMapCMapSpanMkEquivQuotMapCQuotMapSpanMk_symm_quotQuotMk, ringKrullDim_quotient_le, Quotient.smul_top, instIsScalarTowerQuotientHPowKerRingHomAlgebraMapOfNat, liftOfDerivationToSquareZero_mk_apply, Factors.isScalarTower, Quotient.index_eq_zero, Quotient.normal, IsLocalization.Away.mvPolynomialQuotientEquiv_apply, Algebra.Presentation.naive_relation_apply, quotientToQuotientRangePowQuotSucc_mk, absNorm_ne_zero_iff, AlgHom.IsArithFrobAt.apply_of_pow_eq_one, AdjoinRoot.quotEquivQuotMap_apply, finrank_prime_pow_ramificationIdx, Quotient.stabilizerHom_surjective_of_profinite, pi_tensorProductMk_quotient_surjective, PowerSeries.IsWeierstrassDivisorAt.mod'_mk_eq_mod, DoubleQuot.quotQuotEquivQuotOfLE_comp_quotQuotMkₐ, KummerDedekind.emultiplicity_factors_map_eq_emultiplicity, Algebra.FormallySmooth.mk_lift, IsPrimitiveRoot.finite_quotient_span_sub_one', AdicCompletion.factorₐ_evalₐ_one, TensorProduct.tensorQuotEquivQuotSMul_tmul_mk, IsPrimitiveRoot.finite_quotient_span_sub_one, Module.ringKrullDim_quotient_add_one_of_mem_nonZeroDivisors, Algebra.PreSubmersivePresentation.naive_toPresentation, Polynomial.quotientSpanXSubCAlgEquiv_mk, isFiniteLength_quotient_span_singleton, instIsAlgebraicQuotientIdealResidueField, DoubleQuot.ker_quotQuotMk, ringKrullDim_le_ringKrullDim_quotient_add_card, AdicCompletion.mk_ofAlgEquiv_symm, exact_mulQuot_quotOfMul, AlgHom.IsArithFrobAt.restrict_injective, DoubleQuot.coe_quotQuotEquivQuotSupₐ, quotientMulEquivQuotientProd_snd, height_le_ringKrullDim_quotient_add_one, algebraMap_mk, Quotient.stabilizerHom_apply, fst_comp_quotientMulEquivQuotientProd, Quotient.torsionBy_eq_span_singleton, QuotSMulTop.equivQuotTensor_naturality, AdicCompletion.transitionMap_comp_reduceModIdeal, AdicCompletion.instIsScalarTowerQuotientIdealHSMulTopSubmodule, isNoetherian_of_liesOver, tensorKaehlerQuotKerSqEquiv_symm_tmul_D, AlgebraicGeometry.Scheme.IdealSheafData.subschemeι_app, Quotient.exists_algEquiv_fixedPoint_quotient_under, mk_mem_cotangentIdeal, Int.quotientSpanEquivZMod_comp_castRingHom, associatedPrimes.eq_singleton_of_isPrimary, ringKrullDim_le_ringKrullDim_quotient_add_spanFinrank, Quotient.alg_map_eq, module_finite_of_liesOver, exists_integral_inj_algHom_of_quotient, Quotient.stabilizerQuotientInertiaEquiv_mk, quotAdjoinEquivQuotMap_apply_mk, MixedCharZero.charP_quotient, IsPrimitiveRoot.finite_quotient_toInteger_sub_one, quotientToQuotientRangePowQuotSucc_surjective, IsLocalization.Away.quotient_of_isIdempotentElem, WittVector.fontaineThetaModPPow_teichmuller, factorPowSucc.isUnit_of_isUnit_image, Submodule.instIsScalarTowerQuotientSpanSingletonSetSubtypeMemTorsionBy, Valuation.supp_quot, DoubleQuot.coe_quotQuotEquivQuotSupₐ_symm, ker_tensorProductMk_quotient, ringKrullDim_add_length_eq_ringKrullDim_of_isRegular, tensorKaehlerQuotKerSqEquiv_tmul_D, finrank_quotient_map, derivationToSquareZeroEquivLift_symm_apply_apply_coe, WittVector.ghostComponentModPPow_teichmuller_coeff, Quotient.algEquivOfEqComap_apply, DoubleQuot.quotQuotMkₐ_toRingHom, height_le_ringKrullDim_quotient_add_encard, Quotient.algebraMap_quotient_pow_ramificationIdx, DoubleQuot.quotQuotEquivQuotOfLE_symm_comp_mkₐ, IsLocalization.AtPrime.equivQuotMaximalIdeal_apply_mk, TensorProduct.tensorQuotEquivQuotSMul_symm_mk, LinearMap.reduceModIdeal_apply, ringKrullDim_quotient_span_singleton_succ_eq_ringKrullDim_of_mem_nonZeroDivisors, AdjoinRoot.quotEquivQuotMap_apply_mk, PowerBasis.quotientEquivQuotientMinpolyMap_symm_apply, minimalPrimes_eq_comap, ringKrullDim_quotient_succ_le_of_nonZeroDivisor, Polynomial.Monic.finite_quotient, ringKrullDim_quotient_span_singleton_succ_eq_ringKrullDim_of_mem_jacobson, CharP.quotient', idealFactorsEquivOfQuotEquiv_symm, IsLocalization.AtPrime.algebraMap_equivQuotMaximalIdeal_symm_apply, quotOfMul_surjective, AlgebraicGeometry.Scheme.IdealSheafData.isLocalization_away, snd_comp_quotientMulEquivQuotientProd, Quotient.isScalarTower_of_liesOver, DoubleQuot.ker_quotLeftToQuotSup, IsAdicComplete.mk_liftAlgHom, AdjoinRoot.Polynomial.quotQuotEquivComm_mk, quotientInfEquivQuotientProd_snd, radical_eq_jacobson_iff_radical_quotient_eq_jacobson_bot, cotangentEquivIdeal_apply, DoubleQuot.coe_quotQuotEquivQuotOfLEₐ, quotientToQuotientRangePowQuotSucc_injective, EqualCharZero.nonempty_algebraRat_iff, TensorProduct.quotTensorEquivQuotSMul_symm_mk, AlgebraicGeometry.IsClosedImmersion.Spec_iff, RingOfIntegers.ZModXQuotSpanEquivQuotSpan_mk_apply, ringKrullDim_le_ringKrullDim_add_card, AdicCompletion.evalOneₐ_of, Algebra.FormallySmooth.iff_split_surjection, jacobson_eq_iff_jacobson_quotient_eq_bot, Algebra.trace_quotient_mk, polynomialQuotientEquivQuotientPolynomial_symm_mk, Polynomial.IsDistinguishedAt.algEquivQuotient_symm_apply, QuotSMulTop.equivQuotTensor_naturality_mk, Module.equiv_free_prod_directSum, IsAdicComplete.mk_liftRingHom, AlgHom.IsArithFrobAt.card_pos, AdicCompletion.factor_eval_liftRingHom, Algebra.TensorProduct.quotIdealMapEquivTensorQuot_symm_tmul, IsLocalRing.quotient_span_eq_top_iff_span_eq_top, Factors.finrank_pow_ramificationIdx, quotientMulEquivQuotientProd_fst, IsPrimitiveRoot.card_quotient_toInteger_sub_one, DoubleQuot.quotQuotEquivQuotOfLEₐ_comp_mkₐ, Algebra.weaklyQuasiFiniteAt_iff, rank_pow_quot_aux, rootsOfUnityMapQuot_apply, StandardEtalePresentation.toPresentation_σ', AdicCompletion.evalₐ_liftAlgHom, AdicCompletion.surjective_evalₐ, WittVector.quotientPEquiv_mk, instIsIntegralQuotientIdeal, AlgEquiv.prodQuotientOfIsIdempotentElem_apply_snd, AdicCompletion.transitionMap_map_pow, isAssociatedPrime_iff_exists_injective_linearMap, Quotient.ker_stabilizerHom, rank_pow_quot, EqualCharZero.iff_not_mixedCharZero, AdicCompletion.mk_ofAlgEquiv_symm_eq_evalOneₐ, AdjoinRoot.quotAdjoinRootEquivQuotPolynomialQuot_symm_mk_mk, DoubleQuot.quotQuotEquivQuotSup_quotQuotMk, pi_mkQ_rTensor, Quotient.nontrivial_of_liesOver_of_ne_top, DoubleQuot.quotQuotEquivCommₐ_toRingEquiv, DoubleQuot.coe_quotQuotToQuotSupₐ, Quotient.norm_mk_lt, IsLocalRing.basisQuotient_apply, torsionMapQuot_injective, injective_algebraMap_quotient_residueField, Algebra.Generators.naive_σ, trace_quotient_eq_trace_localization_quotient, AdjoinRoot.Polynomial.quotQuotEquivComm_symm_mk_mk, Quotient.algebra_isIntegral_of_liesOver, powQuotSuccInclusion_injective, DoubleQuot.quotQuotEquivQuotSupₐ_toRingEquiv, Algebra.trace_quotient_eq_of_isDedekindDomain, idealFactorsFunOfQuotHom_id, finite_quotient_pow, instIsScalarTowerQuotientIdealResidueField, card_stabilizer_eq_card_inertia_mul_finrank, AdicCompletion.transitionMap_map_mul, Valued.integer.finite_quotient_maximalIdeal_pow_of_finite_residueField, AlgEquiv.prodQuotientOfIsIdempotentElem_apply_fst, Algebra.TensorProduct.quotIdealMapEquivTensorQuot_mk, CharP.quotient, StandardEtalePresentation.toPresentation_algebra_algebraMap_apply, Algebra.FormallyUnramified.quotient, derivationToSquareZeroEquivLift_apply_coe_apply, AdjoinRoot.quotMapOfEquivQuotMapCMapSpanMk_mk, AlgHom.ker_kerSquareLift, height_le_ringKrullDim_quotient_add_spanFinrank, liftOfDerivationToSquareZero_mk_apply', quotientInfEquivQuotientProd_fst, Algebra.FormallySmooth.exists_adicCompletionEvalOneₐ_comp_eq, DoubleQuot.quotQuotEquivQuotOfLEₐ_toRingEquiv, WittVector.quotEquivOfEq_ghostComponentModPPow, AdicCompletion.evalₐ_of, Quotient.isNoetherianRing, AdjoinRoot.quotEquivQuotMap_symm_apply, StandardEtalePresentation.toPresentation_val, isDomain_map_C_quotient, Algebra.instEssFiniteTypeQuotientIdeal, AdjoinRoot.quotMapCMapSpanMkEquivQuotMapCQuotMapSpanMk_mk, topologicalRing_quotient, AdicCompletion.evalOneₐ_surjective, KummerDedekind.normalizedFactors_ideal_map_eq_normalizedFactors_min_poly_mk_map, AdicCompletion.factor_evalₐ_eq_eval, AdicCompletion.evalₐ_comp_liftRingHom, Factors.finiteDimensional_quotient_pow, cotangentEquivIdeal_symm_apply, isJacobsonRing_quotient, Module.supportDim_quotient_eq_ringKrullDim, PowerSeries.IsWeierstrassDivisorAt.mk_mod'_eq_self, ringKrullDim_le_ringKrullDim_add_spanFinrank, Quotient.finite_of_isInvariant, AdicCompletion.evalₐ_mk, DoubleQuot.quotQuotEquivComm_comp_quotQuotMkₐ, IsLocalization.AtPrime.equivQuotientMapMaximalIdeal_apply_mk, Algebra.IsIntegral.quotient, DoubleQuot.quotQuotEquivComm_mk_mk, Module.exists_surjective_quotient_of_finite, AlgHom.IsArithFrobAt.restrict_mk, AdicCompletion.evalₐ_mkₐ, ncard_primesOver_mul_card_inertia_mul_finrank, EqualCharZero.of_algebraRat, DoubleQuot.quotQuotEquivQuotOfLE_symm_comp_mk, TensorProduct.tensorQuotEquivQuotSMul_comp_mk, DoubleQuot.quotQuotEquivQuotSup_symm_quotQuotMk, DoubleQuot.coe_quotQuotEquivCommₐ, StandardEtalePresentation.toPresentation_relation, fst_comp_quotientInfEquivQuotientProd, CharP.quotient_iff_le_ker_natCast, polynomialQuotientEquivQuotientPolynomial_map_mk, PrimeSpectrum.mem_image_comap_zeroLocus_sdiff, DoubleQuot.quotQuotEquivQuotSup_quot_quot_algebraMap, IsLocalization.AtPrime.equivQuotMaximalIdeal_symm_apply_mk, TensorProduct.quotTensorEquivQuotSMul_comp_mk, Algebra.PreSubmersivePresentation.ofHasCoeffs_algebra_smul, DoubleQuot.quotQuotEquivQuotOfLE_symm_mk, AlgebraicGeometry.Scheme.Hom.toImage_app, Algebra.isSeparable_residueField_iff, AlgHom.kerSquareLift_mk, bijective_algebraMap_quotient_residueField, instFiniteDimensionalQuotientPolynomialIdealSpanSingletonSetSmithCoeffs, snd_comp_quotientInfEquivQuotientProd, quotientToQuotientRangePowQuotSuccAux_mk, DoubleQuot.quotLeftToQuotSupₐ_toRingHom, MixedCharZero.reduce_to_maximal_ideal, Factors.piQuotientEquiv_mk, IsLocalRing.finite_quotient_iff, DoubleQuot.quotQuotEquivQuotSupₐ_symm_toRingEquiv, LinearMap.ker_tensorProductMk, ringChar_quot, ringKrullDim_le_ringKrullDim_quotSMulTop_succ, cotangentIdeal_square, CharP.quotient_iff, Polynomial.IsDistinguishedAt.algEquivQuotient_apply, Module.torsion_by_prime_power_decomposition, AddValuation.supp_quot_supp, AddValuation.supp_quot, IsLocalRing.isOpen_iff_finite_quotient, IsDedekindDomain.quotientEquivPiFactors_mk, TensorProduct.quotTensorEquivQuotSMul_symm_comp_mkQ, AdjoinRoot.quotAdjoinRootEquivQuotPolynomialQuot_mk_of, Algebra.FinitePresentation.quotient, instCompactSpaceQuotientIdeal, Algebra.Generators.ker_naive, finiteQuotientOfFreeOfNeBot, AlgebraicGeometry.Scheme.Hom.liftQuotient_comp_assoc, DoubleQuot.coe_liftSupQuotQuotMkₐ, AdicCompletion.evalOneₐ_liftAlgHom, NumberField.Ideal.primesOverSpanEquivMonicFactorsMod_symm_apply, DoubleQuot.quotQuotEquivQuotOfLE_comp_quotQuotMk, AdicCompletion.evalₐ_liftRingHom, Quotient.maximal_ideal_iff_isField_quotient, Int.quotientSpanNatEquivZMod_comp_castRingHom, instFiniteQuotientIdealOfIsMaximal, WittVector.ghostComponentModPPow_map_mk, EqualCharZero.of_not_mixedCharZero, Algebra.Presentation.mem_ker_naive, isRadical_iff_quotient_reduced, AlgHom.IsArithFrobAt.restrict_apply, DoubleQuot.quotQuotEquivQuotOfLE_quotQuotMk, AlgHom.IsArithFrobAt.finite_quotient, to_quotient_square_comp_toCotangent, ringKrullDim_le_ringKrullDim_quotient_add_encard, DoubleQuot.quotQuotEquivComm_symm, Factors.piQuotientEquiv_map, instIsFractionRingQuotientIdealResidueField, TensorProduct.quotTensorEquivQuotSMul_mk_tmul, derivationQuotKerSq_mk, TensorProduct.tensorQuotEquivQuotSMul_symm_comp_mkQ, DoubleQuot.quotQuotEquivComm_algebraMap, Quotient.algebraMap_mk_of_liesOver, KummerDedekind.normalizedFactorsMapEquivNormalizedFactorsMinPolyMk_symm_apply_eq_span, RingQuot.ringQuotToIdealQuotient_apply, IsLocalRing.quotient_artinian_of_mem_minimalPrimes_of_isLocalRing, KummerDedekind.quotMapEquivQuotQuotMap_symm_apply, mulQuot_injective
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