Theorems · Definition · commutative algebra

IsDedekindDomain.idealFactorsFunOfQuotHom

{R : Type u_1} →
  {A : Type u_2} →
    [inst : CommRing R] →
      [inst_1 : CommRing A] →
        [IsDedekindDomain A] →
          {I : Ideal R} →
            {J : Ideal A} → {f : R ⧸ I →+* A ⧸ J} → Function.Surjective ⇑f → { p // p ∣ I } →o { p // p ∣ J }

The map from ideals of R dividing I to the ideals of A dividing J induced by a homomorphism f : R/I →+* A/J

Defined in

Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas

Cited by

7 results in Mathlib

Foundations

Depth 147 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingIsDedekindDomain