Theorems · Theorem · commutative algebra

IsDedekindDomain.HeightOneSpectrum.count_normalizedFactors_eq_multiplicity

∀ {R : Type u_3} [inst : CommRing R] [inst_1 : IsDedekindDomain R] {I : Ideal R},
  I ≠ ⊥ →
    ∀ (p : IsDedekindDomain.HeightOneSpectrum R),
      Multiset.count p.asIdeal (UniqueFactorizationMonoid.normalizedFactors I) = multiplicity p.asIdeal I

Normalize the multiplicity of a prime ideal p in the factorization of I as multiplicity p.asIdeal I.

Defined in

Mathlib.RingTheory.DedekindDomain.Factorization

Cited by

4 results in Mathlib

Foundations

Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingIsDedekindDomain