Theorems · Theorem · commutative algebra

Algebra.intNorm_eq_zero

∀ {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]
  [FiniteDimensional (FractionRing A) (FractionRing B)] {x : B}, (Algebra.intNorm A B) x = 0 ↔ x = 0

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

CommRingCommRingAlgebraIsIntegrallyClosedIsDomainIsDomainIsIntegrallyClosedAlgebra.IsIntegralModule.IsTorsionFreeFiniteDimensional