Theorems · Theorem · commutative algebra

Algebra.intNorm_map_algEquiv

∀ {A : Type u_1} {B : Type u_6} (B₂ : Type u_7) [inst : CommRing A] [inst_1 : CommRing B] [inst_2 : CommRing B₂]
  [inst_3 : Algebra A B] [inst_4 : Algebra A B₂] [inst_5 : IsIntegrallyClosed A] [inst_6 : IsDomain A]
  [inst_7 : IsDomain B] [inst_8 : IsIntegrallyClosed B] [inst_9 : Algebra.IsIntegral A B]
  [inst_10 : Module.IsTorsionFree A B] [inst_11 : IsDomain B₂] [inst_12 : IsIntegrallyClosed B₂]
  [inst_13 : Algebra.IsIntegral A B₂] [inst_14 : Module.IsTorsionFree A B₂]
  [Algebra.IsAlgebraic (FractionRing A) (FractionRing B)] [Algebra.IsAlgebraic (FractionRing A) (FractionRing B₂)]
  (x : B) (σ : B ≃ₐ[A] B₂), (Algebra.intNorm A B₂) (σ x) = (Algebra.intNorm A B) x

Defined in

Mathlib.RingTheory.IntegralClosure.IntegralRestrict

Cited by

0 results in Mathlib

Foundations

Depth 185 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingCommRingAlgebraAlgebraIsIntegrallyClosedIsDomainIsDomainIsIntegrallyClosedAlgebra.IsIntegralModule.IsTorsionFreeIsDomainIsIntegrallyClosedAlgebra.IsIntegralModule.IsTorsionFreeAlgebra.IsAlgebraicAlgebra.IsAlgebraic