Theorems · Theorem · commutative algebra

IsDedekindDomain.idealFactorsFunOfQuotHom_coe_coe

∀ {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} {f : R ⧸ I →+* A ⧸ J} (hf : Function.Surjective ⇑f) (X : { p // p ∣ I }),
  ↑((IsDedekindDomain.idealFactorsFunOfQuotHom hf) X) =
    Ideal.comap (Ideal.Quotient.mk J) (Ideal.map f (Ideal.map (Ideal.Quotient.mk I) ↑X))

Defined in

Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas

Cited by

1 results in Mathlib

Foundations

Depth 148 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingIsDedekindDomain