Theorems · Theorem · commutative algebra

Algebra.intNorm_intNorm

∀ (A : Type u_1) (B : Type u_6) [inst : CommRing A] [inst_1 : CommRing B] [inst_2 : Algebra A B]
  [inst_3 : IsIntegrallyClosed A] [inst_4 : IsDomain A] [inst_5 : IsDomain B] [inst_6 : IsIntegrallyClosed B]
  [inst_7 : Algebra.IsIntegral A B] [inst_8 : Module.IsTorsionFree A B] {C : Type u_9} [inst_9 : CommRing C]
  [inst_10 : IsDomain C] [inst_11 : IsIntegrallyClosed C] [inst_12 : Algebra A C] [inst_13 : Algebra B C]
  [IsScalarTower A B C] [inst_15 : Algebra.IsIntegral A C] [inst_16 : Algebra.IsIntegral B C]
  [inst_17 : Module.IsTorsionFree A C] [inst_18 : Module.IsTorsionFree B C] (x : C),
  (Algebra.intNorm A B) ((Algebra.intNorm B C) x) = (Algebra.intNorm A C) x

Defined in

Mathlib.RingTheory.IntegralClosure.IntegralRestrict

Cited by

2 results in Mathlib

Foundations

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

Assumes

CommRingCommRingAlgebraIsIntegrallyClosedIsDomainIsDomainIsIntegrallyClosedAlgebra.IsIntegralModule.IsTorsionFreeCommRingIsDomainIsIntegrallyClosedAlgebraAlgebraIsScalarTowerAlgebra.IsIntegralAlgebra.IsIntegralModule.IsTorsionFreeModule.IsTorsionFree