Mathlib Map

Theorems · Definition · commutative algebra

Associates.factors

{α : Type u_1} → [inst : CommMonoidWithZero α] → [UniqueFactorizationMonoid α] → Associates α → Associates.FactorSet α

This returns the multiset of irreducible factors of an associate as a FactorSet, a multiset of irreducible associates WithTop.

Defined in
Mathlib.RingTheory.UniqueFactorizationDomain.FactorSet
Cited by
97 results in Mathlib
Foundations
Depth 30 from the axioms, rests on 531 definitions · uses propext, Classical.choice, Quot.sound
Assumes
CommMonoidWithZeroUniqueFactorizationMonoid

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

FractionalIdeal.count · cited by 25FractionalIdeal.countIsDedekindDomain.HeightOneSpectrum.maxPowDividing · cited by 17HeightOneSpectrum.maxPowD…Associates.factors_mk · cited by 12Associates.factors_mkIsDedekindDomain.HeightOneSpectrum.intValuation_if_neg · cited by 11HeightOneSpectrum.intValu…IsDedekindDomain.HeightOneSpectrum.intValuationDef · cited by 9HeightOneSpectrum.intValu…IsDedekindDomain.HeightOneSpectrum.intValuation_le_one · cited by 9HeightOneSpectrum.intValu…Associates.factors_prod · cited by 9Associates.factors_prodIdeal.hasFiniteMulSupport · cited by 7Ideal.hasFiniteMulSupportAssociates.count_mul · cited by 7Associates.count_mulAssociates.factors_zero · cited by 7Associates.factors_zeroAssociates.prime_pow_dvd_iff_le · cited by 7Associates.prime_pow_dvd_…Associates.factors_one · cited by 6Associates.factors_oneIdeal.finprod_heightOneSpectrum_factorization · cited by 6Ideal.finprod_heightOneSp…IsDedekindDomain.HeightOneSpectrum.intValuation_le_pow_iff_dvd · cited by 5HeightOneSpectrum.intValu…Associates.count_ne_zero_iff_dvd · cited by 5Associates.count_ne_zero_…Top.top · cited by 9680Top.topWithTop.some · cited by 1128WithTop.someCommMonoidWithZero · cited by 913CommMonoidWithZeroUniqueFactorizationMonoid · cited by 279UniqueFactorizationMonoidAssociates · cited by 210AssociatesAssociates.FactorSet · cited by 52Associates.FactorSetAssociates.factors' · cited by 15Associates.factors'Associated.setoid · cited by 10Associated.setoidAssociates.factorsCITED BYCITES

Cites8

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Cited by101

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