Theorems · Theorem · commutative algebra

IsDedekindDomain.primesOver_ncard_ne_zero

∀ {A : Type u_4} [inst : CommRing A] (p : Ideal A) [hpm : p.IsMaximal] (B : Type u_5) [inst_1 : CommRing B]
  [IsDedekindDomain B] [inst_3 : Algebra A B] [IsDomain A] [Module.IsTorsionFree A B] [Algebra.IsIntegral A B],
  (p.primesOver B).ncard ≠ 0

Defined in

Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas

Cited by

4 results in Mathlib

Foundations

Depth 153 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingIdeal.IsMaximalCommRingIsDedekindDomainAlgebraIsDomainModule.IsTorsionFreeAlgebra.IsIntegral