Theorems · Theorem · commutative algebra

IsDedekindDomain.HeightOneSpectrum.maxPowDividing_eq_pow_multiset_count

∀ {R : Type u_1} [inst : CommRing R] [inst_1 : IsDedekindDomain R] (v : IsDedekindDomain.HeightOneSpectrum R)
  {I : Ideal R},
  I ≠ 0 → v.maxPowDividing I = v.asIdeal ^ Multiset.count v.asIdeal (UniqueFactorizationMonoid.normalizedFactors I)

Defined in: Mathlib.RingTheory.DedekindDomain.Factorization
Cited by: 2 results in Mathlib
Foundations: Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing IsDedekindDomain

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Cites24

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CommRingstatement and proof · cited by 17,173
Idealstatement and proof · cited by 4,748
Multisetproof · cited by 2,627
Multiset.mapproof · cited by 876
IsDedekindDomainstatement and proof · cited by 668
IsDedekindDomain.HeightOneSpectrumstatement and proof · cited by 338
Multiset.countstatement and proof · cited by 302
Subtype.val_injectiveproof · cited by 232
Associatesproof · cited by 210
IsDedekindDomain.HeightOneSpectrum.asIdealstatement and proof · cited by 156
UniqueFactorizationMonoid.normalizedFactorsstatement and proof · cited by 151
Associates.mkproof · cited by 137

Cited by2

Results whose statement or proof uses this declaration.

Ideal.map_algebraMap_eq_finsetProd_powproof · cited by 2
IsDedekindDomain.HeightOneSpectrum.maxPowDividing_eq_pow_multiplicityproof · cited by 2