Theorems · Definition · commutative algebra
UniqueFactorizationMonoid.normalizedFactors
{α : Type u_1} →
[inst : CommMonoidWithZero α] → [NormalizationMonoid α] → [UniqueFactorizationMonoid α] → α → Multiset αNoncomputably determines the multiset of prime factors.
- Cited by
- 151 results in Mathlib
- Foundations
- Depth 20 from the axioms, rests on 214 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Multisetstatement · cited by 2,627
- CommMonoidWithZerostatement and proof · cited by 913
- Multiset.mapproof · cited by 876
- UniqueFactorizationMonoidstatement and proof · cited by 279
- NormalizationMonoidstatement and proof · cited by 165
- normalizeproof · cited by 137
- UniqueFactorizationMonoid.factorsproof · cited by 55
Cited by162
Results whose statement or proof uses this declaration.
- UniqueFactorizationMonoid.primeFactorsproof · cited by 32
- UniqueFactorizationMonoid.prime_of_normalized_factorstatement · cited by 23
- UniqueFactorizationMonoid.prod_normalizedFactorsstatement · cited by 23
- UniqueFactorizationMonoid.dvd_of_mem_normalizedFactorsstatement and proof · cited by 20
- UniqueFactorizationMonoid.irreducible_of_normalized_factorstatement and proof · cited by 15
- UniqueFactorizationMonoid.emultiplicity_eq_count_normalizedFactorsstatement and proof · cited by 14
- UniqueFactorizationMonoid.normalizedFactors_zerostatement · cited by 14
- UniqueFactorizationMonoid.dvd_iff_normalizedFactors_le_normalizedFactorsstatement and proof · cited by 11
- UniqueFactorizationMonoid.normalizedFactors_mulstatement and proof · cited by 11
- UniqueFactorizationMonoid.normalizedFactors_irreduciblestatement and proof · cited by 10
- RingOfIntegers.monicFactorsModproof · cited by 10
- UniqueFactorizationMonoid.normalize_normalized_factorstatement · cited by 9