Theorems · Definition · commutative algebra

IsDedekindDomain.idealFactorsEquivOfQuotEquiv

{R : Type u_1} →
  {A : Type u_2} →
    [inst : CommRing R] →
      [inst_1 : CommRing A] →
        [IsDedekindDomain A] →
          {I : Ideal R} → {J : Ideal A} → [IsDedekindDomain R] → R ⧸ I ≃+* A ⧸ J → ↑{p | p ∣ I} ≃o ↑{p | p ∣ J}

The bijection between ideals of R dividing I and the ideals of A dividing J induced by an isomorphism f : R/I ≅ A/J.

Defined in

Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas

Cited by

9 results in Mathlib

Foundations

Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingIsDedekindDomainIsDedekindDomain