Theorems · Theorem · commutative algebra

Algebra.dvd_algebraMap_intNorm_self

∀ (A : Type u_1) (B : Type u_6) [inst : CommRing A] [inst_1 : CommRing B] [inst_2 : Algebra A B] [inst_3 : IsDomain A]
  [inst_4 : IsIntegrallyClosed A] [inst_5 : IsDomain B] [inst_6 : IsIntegrallyClosed B] [inst_7 : Module.Finite A B]
  [inst_8 : Module.IsTorsionFree A B] (x : B), x ∣ (algebraMap A B) ((Algebra.intNorm A B) x)

Defined in

Mathlib.RingTheory.IntegralClosure.IntegralRestrict

Cited by

1 results in Mathlib

Foundations

Depth 186 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraIsDomainIsIntegrallyClosedIsDomainIsIntegrallyClosedModule.FiniteModule.IsTorsionFree