Theorems · Theorem · commutative algebra

IsDedekindDomain.idealFactorsFunOfQuotHom_comp

∀ {R : Type u_1} {A : Type u_2} [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : IsDedekindDomain A] {I : Ideal R}
  {J : Ideal A} {B : Type u_4} [inst_3 : CommRing B] [inst_4 : IsDedekindDomain B] {L : Ideal B} {f : R ⧸ I →+* A ⧸ J}
  {g : A ⧸ J →+* B ⧸ L} (hf : Function.Surjective ⇑f) (hg : Function.Surjective ⇑g),
  (IsDedekindDomain.idealFactorsFunOfQuotHom hg).comp (IsDedekindDomain.idealFactorsFunOfQuotHom hf) =
    IsDedekindDomain.idealFactorsFunOfQuotHom ⋯

Defined in

Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas

Cited by

1 results in Mathlib

Foundations

Depth 149 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingIsDedekindDomainCommRingIsDedekindDomain