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Theorems · Theorem · field theory

Algebra.FormallyUnramified.isRadical_map_isMaximal

∀ (A : Type u_2) [inst : CommRing A] (B : Type u_4) [inst_1 : CommRing B] [inst_2 : Algebra A B]
  [Algebra.EssFiniteType A B] [Algebra.FormallyUnramified A B] (p : Ideal A) [p.IsMaximal],
  (Ideal.map (algebraMap A B) p).IsRadical
Defined in
Mathlib.RingTheory.Unramified.Field
Cited by
1 results in Mathlib
Foundations
Depth 181 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingCommRingAlgebraAlgebra.EssFiniteTypeAlgebra.FormallyUnramifiedIdeal.IsMaximal
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

isDedekindDomainDvr.of_formallyUnramified · cited by 1isDedekindDomainDvr.of_fo…CommRing · cited by 17173CommRingAlgebra · cited by 11388AlgebraRingHom · cited by 10189RingHomField · cited by 7404FieldIdeal · cited by 4748IdealAlgebra.algebraMap · cited by 4706Algebra.algebraMapHasQuotient.Quotient · cited by 2301HasQuotient.QuotientIdeal.map · cited by 692Ideal.mapIdeal.IsMaximal · cited by 452Ideal.IsMaximalAlgebra.FormallyUnramified · cited by 75Algebra.FormallyUnramifiedAlgebra.EssFiniteType · cited by 68Algebra.EssFiniteTypeIdeal.IsRadical · cited by 30Ideal.IsRadicalIdeal.Quotient.field · cited by 25Quotient.fieldAlgebra.FormallyUnramified.isReduced_of_field · cited by 6FormallyUnramified.isRedu…Ideal.isRadical_iff_quotient_reduced · cited by 4Ideal.isRadical_iff_quoti…FormallyUnramified.isRadical_…CITED BYCITES

Cites15

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Cited by1

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