Theorems · Theorem · commutative algebra

Algebra.algebraMap_intNorm

∀ {A : Type u_1} {K : Type u_2} {L : Type u_3} {B : Type u_6} [inst : CommRing A] [inst_1 : CommRing B]
  [inst_2 : Algebra A B] [inst_3 : Field K] [inst_4 : Field L] [inst_5 : Algebra A K] [IsFractionRing A K]
  [inst_7 : Algebra K L] [inst_8 : Algebra A L] [IsScalarTower A K L] [inst_10 : Algebra B L] [IsScalarTower A B L]
  [IsIntegralClosure B A L] [FiniteDimensional K L] [inst_14 : IsIntegrallyClosed A] [inst_15 : IsDomain A]
  [inst_16 : IsDomain B] [inst_17 : IsIntegrallyClosed B] [inst_18 : Algebra.IsIntegral A B]
  [inst_19 : Module.IsTorsionFree A B] (x : B),
  (algebraMap A K) ((Algebra.intNorm A B) x) = (Algebra.norm K) ((algebraMap B L) x)

Defined in

Mathlib.RingTheory.IntegralClosure.IntegralRestrict

Cited by

4 results in Mathlib

Foundations

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

Assumes

CommRingCommRingAlgebraFieldFieldAlgebraIsFractionRingAlgebraAlgebraIsScalarTowerAlgebraIsScalarTowerIsIntegralClosureFiniteDimensionalIsIntegrallyClosedIsDomainIsDomainIsIntegrallyClosedAlgebra.IsIntegralModule.IsTorsionFree