Theorems · Theorem · commutative algebra

Algebra.algebraMap_intNorm_fractionRing

∀ {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] (x : B),
  (algebraMap A (FractionRing A)) ((Algebra.intNorm A B) x) =
    (Algebra.norm (FractionRing A)) ((algebraMap B (FractionRing B)) x)

Defined in

Mathlib.RingTheory.IntegralClosure.IntegralRestrict

Cited by

6 results in Mathlib

Foundations

Depth 184 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraIsIntegrallyClosedIsDomainIsDomainIsIntegrallyClosedAlgebra.IsIntegralModule.IsTorsionFree