Theorems · Theorem · commutative algebra

IsDedekindDomain.mem_primesOverFinset_iff

∀ {A : Type u_4} [inst : CommRing A] {p : Ideal A},
  p ≠ ⊥ →
    ∀ [hpm : p.IsMaximal] (B : Type u_5) [inst_1 : CommRing B] [inst_2 : IsDedekindDomain B] [inst_3 : Algebra A B]
      [IsDomain A] [Module.IsTorsionFree A B] {P : Ideal B},
      P ∈ IsDedekindDomain.primesOverFinset p B ↔ P ∈ p.primesOver B

Defined in

Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas

Cited by

4 results in Mathlib

Foundations

Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingIdeal.IsMaximalCommRingIsDedekindDomainAlgebraIsDomainModule.IsTorsionFree