Subalgebra 📖 | CompData | 868 mathmath: IsPrimitiveRoot.subOneIntegralPowerBasis_gen_prime, Subalgebra.mem_restrictScalars, IsCyclotomicExtension.adjoin_primitive_root_eq_top, Algebra.IsUnramifiedAt.exists_primesOver_under_adjoin_eq_singleton_and_residueField_bijective, Algebra.range_ofId, exists_fg_and_mem_baseChange, StarSubalgebra.mem_toSubalgebra, Subalgebra.LinearDisjoint.inf_eq_bot, Subalgebra.mulMap_comm, AlgHom.mem_range_self, Submodule.rTensorOne_symm_apply, minpoly.ToAdjoin.injective, Algebra.RingHom.adjoin_algebraMap_apply, Ideal.Filtration.submodule_closure_single, Subalgebra.centralizer_tensorProduct_eq_center_tensorProduct_right, Localization.subalgebra.isLocalization_subalgebra, Ideal.Filtration.submodule_eq_span_le_iff_stable_ge, Algebra.lift_cardinalMk_adjoin_le, IntermediateField.adjoin_eq_top_iff_of_isAlgebraic, StarAlgEquiv.ofInjective_symm_apply, integralClosure_le_span_dualBasis, Polynomial.mem_lifts_iff_mem_alg, Subalgebra.adjoin_rank_le, 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ContinuousMap.comp_attachBound_mem_closure, Algebra.adjoin_restrictScalars, mem_coeSubmodule_conductor, isCyclotomicExtension_iff, AlgEquiv.ofLeftInverse_symm_apply, Subalgebra.range_subset, Subalgebra.LinearDisjoint.val_mulMap_tmul, minpoly.equivAdjoin_toAlgHom, RingCon.quotientKerEquivRangeₐ_mkₐ, MvPolynomial.esymmAlgHom_apply, Subalgebra.mulMap_range, MvPolynomial.irreducible_toPolynomialAdjoinImageCompl, Algebra.elemental.isClosed, RingOfIntegers.exponent_eq_one_iff, Subalgebra.centralizer_coe_range_includeLeft_eq_center_tensorProduct, AlgebraicIndependent.aevalEquiv_apply_coe, Subalgebra.rTensorBot_symm_apply, Algebra.comap_top, AlgHom.subalgebraMap_surjective, Subalgebra.LinearDisjoint.rank_inf_eq_one_of_flat_right_of_inj, StarSubalgebra.sInf_toSubalgebra, Algebra.RingHom.adjoin_algebraMap_surjective, IsAlgebraic.exists_nonzero_eq_adjoin_mul, Subalgebra.instSubsemiringClass, Algebra.TensorProduct.linearEquivIncludeRange_symm_toLinearMap, MaximalSpectrum.iInf_localization_eq_bot, Algebra.IsCentral.center_eq_bot, Subalgebra.range_comp_val, Subalgebra.le_saturation, Subalgebra.centralizer_coe_sup, Submodule.lTensorOne_symm_apply, Subalgebra.coe_eq_zero, MvPolynomial.supported_empty, IsCyclotomicExtension.iff_adjoin_eq_top, Subalgebra.coe_starClosure, AlgebraicIndependent.option_iff, IntermediateField.algebraAdjoinAdjoin.instIsScalarTowerSubtypeMemSubalgebraAdjoinAdjoin, Algebra.mem_ideal_map_adjoin, Subalgebra.coe_unop, Subalgebra.instIsScalarTowerSubtypeMem, Algebra.adjoin_eq, JacobsonNoether.exists_separable_and_not_isCentral', IntermediateField.toSubalgebra_iSup_of_directed, IsPowMul.restriction, Submodule.lTensorOne'_one_tmul, AlgebraicIndependent.matroid_closure_eq, minpoly.coe_equivAdjoin, AlgebraicIndependent.integralClosure, Algebra.adjoin.powerBasis'_minpoly_gen, Algebra.instFiniteTypeSubtypeMemSubalgebraSubalgebra, ContinuousAlgHom.coe_rangeRestrict, Subalgebra.toIsOrderedRing, CliffordAlgebra.even.lift.aux_apply, CliffordAlgebra.even.lift.aux_ι, Algebra.eq_top_iff, Subalgebra.subsingleton_of_subsingleton, Algebra.adjoin_iUnion, Subalgebra.rank_eq_one_iff, Subalgebra.prod_top, mem_reesAlgebra_iff, FunctionField.ringOfIntegers.instIsNoetherianPolynomialSubtypeMemSubalgebraOfIsSeparableRatFunc, IsPrimitiveRoot.subOneIntegralPowerBasisOfPrimePow_gen, Subalgebra.map_comap_eq, Subalgebra.coe_toSubmodule, Subalgebra.FG.small, subalgebra_top_finrank_eq_submodule_top_finrank, IntermediateField.adjoin_eq_top_iff, CommRingCat.Under.equalizerFork_ι, Valuation.Integers.integralClosure, IntermediateField.toSubalgebra_lt_toSubalgebra, IsCyclotomicExtension.Rat.adjoin_singleton_eq_top, Subalgebra.opEquiv_symm_apply, Algebra.IsUnramifiedAt.exists_notMem_forall_ne_mem_and_adjoin_eq_top, IsLocalization.integralClosure, polynomialFunctions.topologicalClosure, Unitization.lift_range_le, RingCon.range_mkₐ, Algebra.adjoin_eq_sInf, AlgebraicIndependent.matroid_isFlat_iff, Subalgebra.natCast_mem, Subalgebra.algebraMap_mem, Algebra.map_top, Subalgebra.linearEquivOp_symm_apply_coe, Subalgebra.mem_star_iff, mem_adjoin_of_dvd_coeff_of_dvd_aeval, Algebra.TensorProduct.algEquivIncludeRange_symm_toAlgHom, IsPrimitiveRoot.self_sub_one_pow_dvd_order, Subalgebra.coe_add, Submodule.lTensorOne_tmul, Algebra.coe_inf, Subalgebra.comm_trans_lTensorBot, AlgHom.coe_equalizer, IsPrimitiveRoot.coe_toInteger, Algebra.adjoin_eq_top_of_intermediateField, CliffordAlgebra.evenEquivEvenNeg_symm_apply, minpoly.instIsScalarTowerSubtypeMemSubringSubalgebraIntegralClosure, integralClosure.isDedekindDomain_fractionRing, Subalgebra.bot_eq_top_of_finrank_eq_one, Subalgebra.restrictScalars_toSubmodule, ContinuousMap.polynomial_comp_attachBound, IsPrimitiveRoot.adjoin_isCyclotomicExtension, StarAlgebra.adjoin_eq_span, Algebra.exists_etale_isIdempotentElem_forall_liesOver_eq_aux, MvPolynomial.supported_univ, IntermediateField.coe_type_toSubalgebra, Submodule.iSup_eq_toSubmodule_range, conductor_eq_top_iff_adjoin_eq_top, CliffordAlgebra.ofEven_ι, Subalgebra.isAlgebraic_bot_iff, AlgebraicIndependent.iff_adjoin_image, instSMulCommClassSubtypeMemSubalgebraIntegralClosure, Subalgebra.toSubring_subtype, AdjoinRoot.adjoinRoot_eq_top, Subalgebra.isSimpleOrder_of_finrank_prime, IntermediateField.algebraicIndependent_adjoin_iff, instIsDomainSubtypeMemSubalgebraIntegralClosure, integralClosure.isIntegral, IntermediateField.rank_eq_rank_subalgebra, MvPolynomial.mem_symmetricSubalgebra, Subalgebra.instCanLiftSetCoeAndForallForallForallMemForallHAddForallForallForallForallHMulForallCoeRingHomAlgebraMap, Set.integer_valuation_le_one, Subalgebra.continuousSMul, Subalgebra.setRange_algebraMap, IntermediateField.toSubalgebra_strictMono, IsIntegral.fg_adjoin_singleton, Subalgebra.centralizer_coe_image_includeLeft_eq_center_tensorProduct, IsScalarTower.subalgebra', Algebra.cardinalMk_adjoin_le, Subalgebra.algebraMap_apply, Subalgebra.smul_def, Complex.adjoin_I, integralClosure.isIntegralClosure, MvPolynomial.esymmAlgHom_fin_bijective, IsCyclotomicExtension.adjoin_roots, instFiniteTypeSubtypePolynomialMemSubalgebraReesAlgebraOfIsNoetherianRing, MvPolynomial.esymmAlgEquiv_apply, IsFractionRing.liftAlgHom_fieldRange, Algebra.FiniteType.out, polynomialFunctions_closure_eq_top', Subalgebra.val_mulMap'_tmul, Subalgebra.mem_pi, IntermediateField.sup_toSubalgebra_of_right, IntermediateField.algebraAdjoinAdjoin.instFaithfulSMulSubtypeMemSubalgebraAdjoinAdjoin, MvPolynomial.range_mapAlgHom, Subalgebra.pointwise_smul_toSubsemiring, IntermediateField.equivOfEq_apply, ContinuousMap.polynomial_comp_attachBound_mem, IntermediateField.le_sup_toSubalgebra, Subalgebra.isAlgebraic_iff, IntermediateField.isAlgebraic_adjoin_iff_bot, Algebra.adjoin_union_eq_adjoin_adjoin, Localization.localRingHom_bijective_of_not_conductor_le, IsTranscendenceBasis.isAlgebraic, StarSubalgebra.coe_toSubalgebra, AlgHom.isNoetherianRing_range, Polynomial.aeval_mem_adjoin_singleton, IntermediateField.transcendental_adjoin_iff, Subalgebra.mem_prod, FiniteDimensional.subalgebra_toSubmodule, IntermediateField.algebraAdjoinAdjoin.instIsScalarTowerSubtypeMemSubalgebraAdjoinAdjoin_1, Subalgebra.mem_perfectClosure_iff, Algebra.adjoin.powerBasis'_gen, MvPolynomial.transcendental_supported_polynomial_aeval_X_iff, Subalgebra.range_le, AlgHom.mem_equalizer, Subalgebra.isDomain, Subalgebra.LinearDisjoint.isDomain, ContinuousAlgHom.instCompleteSpaceSubtypeMemSubalgebraEqualizerOfT2SpaceOfContinuousMapClass, IntermediateField.sup_toSubalgebra_of_isAlgebraic_right, Subalgebra.mem_toSubring, IntermediateField.toSubalgebra_le_toSubalgebra, isNoetherianRing_of_fg, IsAlgClosed.isAlgClosure_of_transcendence_basis, Submodule.lTensorOne_one_tmul, Submodule.mem_toSubalgebra, IsCyclotomicExtension.union_right, Subalgebra.toSubsemiring_subtype, IntermediateField.instIsScalarTowerSubtypeMemSubalgebraAdjoinSingletonSetAdjoinCoeRingHomAlgebraMap, IsIntegral.inv_mem_adjoin, Algebra.map_iInf, Subalgebra.equivOfEq_symm, Algebra.essFiniteType_iff, Subalgebra.coe_centralizer, Algebra.EssFiniteType.cond, ContinuousMap.exists_mem_subalgebra_near_continuous_of_separatesPoints, Subalgebra.isIntegral_iff, Algebra.TensorProduct.adjoin_tmul_eq_top, Subalgebra.pointwise_smul_toSubmodule, IntermediateField.iInf_toSubalgebra, IsCyclotomicExtension.Rat.isIntegralClosure_adjoin_singleton, Subalgebra.mulMap_tmul, AlgEquiv.subalgebraMap_symm_apply_coe, Subalgebra.coe_toSubring, Algebra.mem_inf, Subalgebra.one_mem, Subalgebra.coe_pow, Subalgebra.finrank_bot, MvPolynomial.supportedEquivMvPolynomial_symm_C, Subalgebra.prod_toSubmodule, Subalgebra.le_op_iff, Algebra.coe_sInf, Algebra.sup_def, Subalgebra.restrictScalars_top, Subalgebra.LinearDisjoint.adjoin_rank_eq_rank_right, Algebra.IsCentral.out, polynomialFunctions_closure_eq_top, AlgebraicGeometry.Scheme.Hom.normalizationObjIso_hom_val, IsDedekindDomain.integer_univ, CliffordAlgebra.evenToNeg_comp_evenToNeg, MvPolynomial.isAlgebraic_of_mem_vars_of_forall_totalDegree_le, Algebra.exists_notMem_and_isIntegral_forall_mem_of_ne_of_liesOver, IsAdjoinRoot.adjoin_root_eq_top, Subalgebra.mopAlgEquivOp_apply_coe, instIsAlgebraicSubtypeMemSubalgebraAlgebraicClosure, MvPolynomial.transcendental_supported_X, Subalgebra.coe_mk, IsLocalization.Away.integralClosure, Subalgebra.star_mono, Subalgebra.isClosed_topologicalClosure, Subalgebra.LinearDisjoint.mulLeftMap_ker_eq_bot_iff_linearIndependent_op, Subalgebra.algEquivOpMop_symm_apply_coe, CyclotomicRing.eq_adjoin_primitive_root, Subalgebra.bot_eq_top_iff_rank_eq_one, AlgHom.equalizer_toSubmodule, Subalgebra.rTensorBot_tmul, Subalgebra.LinearDisjoint.rank_eq_one_of_flat_of_self_of_inj, Subalgebra.pi_toSubmodule, Algebra.range_id, Polynomial.SplittingField.adjoin_rootSet, Subalgebra.range_algebraMap, AlgebraicIndependent.iff_transcendental_adjoin_image, TrivSqZeroExt.range_inlAlgHom_sup_adjoin_range_inr, Polynomial.adjoin_X, Algebra.inf_toSubsemiring, StarSubalgebra.iInf_toSubalgebra, Module.End.exists_isNilpotent_isSemisimple, isTranscendenceBasis_iff_algebraicIndependent_isAlgebraic, instSMulCommClassQuotientSubgroupSubtypeMemSubalgebraSubalgebra, StarSubalgebra.top_toSubalgebra, integralClosure.mem_lifts_of_monic_of_dvd_map, IsCyclotomicExtension.lcm_sup, Subalgebra.LinearDisjoint.eq_bot_of_self, Subalgebra.pointwise_smul_toSubring, Subalgebra.op_le_op_iff, Subalgebra.LinearDisjoint.bot_left, Subalgebra.topologicalClosure_adjoin_le_centralizer_centralizer, Subalgebra.rank_bot, Subalgebra.coe_valA', Subalgebra.LinearDisjoint.bot_right, MvPolynomial.supported_eq_vars_subset, AlgebraicGeometry.Scheme.Hom.fromNormalization_app, notMem_iff_exists_ne_and_isConjRoot, Algebra.gc, Subalgebra.rank_toSubmodule, Transcendental.integralClosure, Algebra.adjoin_empty, Subalgebra.fg_bot_toSubmodule, Algebra.botEquiv_symm_apply, RingCon.coe_quotientKerEquivRangeₐ_mkₐ, Ideal.Filtration.submodule_fg_iff_stable, Module.End.mem_subalgebraCenter_iff, Subalgebra.rank_top, Subalgebra.bot_eq_top_of_rank_eq_one, Algebra.TensorProduct.linearEquivIncludeRange_tmul, Algebra.Smooth.exists_subalgebra_fg, Subalgebra.opEquiv_apply, Subalgebra.finrank_eq_one_iff, MvPolynomial.esymmAlgHom_surjective, CommRingCat.Under.equalizer_comp, IntermediateField.algebra_adjoin_le_adjoin, Subalgebra.centralizer_range_includeRight_eq_center_tensorProduct, subalgebra_top_rank_eq_submodule_top_rank, MvPolynomial.esymmAlgEquiv_symm_apply, Subalgebra.equivOfEq_trans, TrivSqZeroExt.range_liftAux, Localization.mem_range_mapToFractionRing_iff, CommRingCat.Under.equalizerFork'_ι, Algebra.IsStandardSmoothOfRelativeDimension.exists_subalgebra_fg, FunctionField.ringOfIntegers.not_isField, CliffordAlgebra.even.lift.aux_one, Subalgebra.eq_bot_of_isPurelyInseparable_of_isSeparable, Subalgebra.finite_bot, MvPolynomial.esymmAlgHom_injective, Algebra.Subalgebra.restrictScalars_adjoin, Algebra.self_mem_adjoin_singleton, Subalgebra.ext_iff, Subalgebra.coe_prod, Algebra.rank_adjoin_le, MvPolynomial.renameSymmetricSubalgebra_apply_coe, CliffordAlgebra.even.lift.aux_algebraMap, Subalgebra.unop_iSup, Subalgebra.unop_sInf, MvPolynomial.transcendental_supported_polynomial_aeval_X, Localization.subalgebra.instIsFractionRingSubtypeMemSubalgebra, Algebra.ZariskisMainProperty.exists_fg_and_exists_notMem_and_awayMap_bijective, Subalgebra.mem_centralizer_iff
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