Theorems · Definition · commutative algebra
Associates.factors
{α : Type u_1} → [inst : CommMonoidWithZero α] → [UniqueFactorizationMonoid α] → Associates α → Associates.FactorSet αThis returns the multiset of irreducible factors of an associate as a FactorSet,
a multiset of irreducible associates WithTop.
- Cited by
- 97 results in Mathlib
- Foundations
- Depth 30 from the axioms, rests on 531 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topproof · cited by 9,680
- WithTop.someproof · cited by 1,128
- CommMonoidWithZerostatement and proof · cited by 913
- UniqueFactorizationMonoidstatement and proof · cited by 279
- Associatesstatement and proof · cited by 210
- Associates.FactorSetstatement · cited by 52
- Associates.factors'proof · cited by 15
- Associated.setoidproof · cited by 10
Cited by101
Results whose statement or proof uses this declaration.
- FractionalIdeal.countproof · cited by 25
- IsDedekindDomain.HeightOneSpectrum.maxPowDividingproof · cited by 17
- Associates.factors_mkstatement · cited by 12
- IsDedekindDomain.HeightOneSpectrum.intValuation_if_negstatement · cited by 11
- IsDedekindDomain.HeightOneSpectrum.intValuationDefproof · cited by 9
- IsDedekindDomain.HeightOneSpectrum.intValuation_le_oneproof · cited by 9
- Associates.factors_prodstatement · cited by 9
- Ideal.hasFiniteMulSupportproof · cited by 7
- Associates.count_mulstatement and proof · cited by 7
- Associates.factors_zerostatement · cited by 7
- Associates.prime_pow_dvd_iff_lestatement and proof · cited by 7
- Associates.factors_onestatement · cited by 6