Theorems · Theorem · commutative algebra

Ideal.relNorm_map_algEquiv

∀ {R : Type u_1} [inst : CommRing R] [inst_1 : IsDomain R] {S : Type u_3} [inst_2 : CommRing S] [inst_3 : IsDomain S]
  [inst_4 : IsIntegrallyClosed R] [inst_5 : IsIntegrallyClosed S] [inst_6 : Algebra R S] [inst_7 : Module.Finite R S]
  [inst_8 : Module.IsTorsionFree R S] [inst_9 : IsDedekindDomain R] [inst_10 : IsDedekindDomain S] {T : Type u_4}
  [inst_11 : CommRing T] [inst_12 : IsDedekindDomain T] [inst_13 : IsIntegrallyClosed T] [inst_14 : Algebra R T]
  [inst_15 : Module.Finite R T] [inst_16 : Module.IsTorsionFree R T] (σ : S ≃ₐ[R] T) (I : Ideal S),
  (Ideal.relNorm R) (Ideal.map σ I) = (Ideal.relNorm R) I

Defined in

Mathlib.RingTheory.Ideal.Norm.RelNorm

Cited by

2 results in Mathlib

Foundations

Depth 192 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingIsDomainCommRingIsDomainIsIntegrallyClosedIsIntegrallyClosedAlgebraModule.FiniteModule.IsTorsionFreeIsDedekindDomainIsDedekindDomainCommRingIsDedekindDomainIsIntegrallyClosedAlgebraModule.FiniteModule.IsTorsionFree