Theorems · Theorem · commutative algebra

idealFactorsEquivOfQuotEquiv_mem_normalizedFactors_of_mem_normalizedFactors

Deprecated since 2026-04-16Use IsDedekindDomain.idealFactorsEquivOfQuotEquiv_mem_normalizedFactors_of_mem_normalizedFactors instead.

∀ {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} [inst_3 : IsDedekindDomain R] (f : R ⧸ I ≃+* A ⧸ J),
  J ≠ ⊥ →
    ∀ {L : Ideal R} (hL : L ∈ UniqueFactorizationMonoid.normalizedFactors I),
      ↑((IsDedekindDomain.idealFactorsEquivOfQuotEquiv f) ⟨L, ⋯⟩) ∈ UniqueFactorizationMonoid.normalizedFactors J

Alias of IsDedekindDomain.idealFactorsEquivOfQuotEquiv_mem_normalizedFactors_of_mem_normalizedFactors.

Defined in

Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas

Cited by

0 results in Mathlib

Foundations

Depth 154 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingIsDedekindDomainIsDedekindDomain