Theorems · Theorem · commutative algebra

IsDedekindDomain.normalizedFactorsEquivOfQuotEquiv_emultiplicity_eq_emultiplicity

∀ {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) (hI : I ≠ ⊥) (hJ : J ≠ ⊥) (L : Ideal R)
  (hL : L ∈ UniqueFactorizationMonoid.normalizedFactors I),
  emultiplicity (↑((IsDedekindDomain.normalizedFactorsEquivOfQuotEquiv f hI hJ) ⟨L, hL⟩)) J = emultiplicity L I

The map normalizedFactorsEquivOfQuotEquiv preserves multiplicities.

Defined in

Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas

Cited by

2 results in Mathlib

Foundations

Depth 160 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingIsDedekindDomainIsDedekindDomain