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Theorems · Definition · commutative algebra

UniqueFactorizationMonoid.normalizedFactors

{α : Type u_1} →
  [inst : CommMonoidWithZero α] → [NormalizationMonoid α] → [UniqueFactorizationMonoid α] → α → Multiset α

Noncomputably determines the multiset of prime factors.

Defined in
Mathlib.RingTheory.UniqueFactorizationDomain.NormalizedFactors
Cited by
151 results in Mathlib
Foundations
Depth 20 from the axioms, rests on 214 definitions · uses propext, Classical.choice, Quot.sound
Assumes
CommMonoidWithZeroNormalizationMonoidUniqueFactorizationMonoid

Around this declaration

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

UniqueFactorizationMonoid.primeFactors · cited by 32UniqueFactorizationMonoid…UniqueFactorizationMonoid.prime_of_normalized_factor · cited by 23UniqueFactorizationMonoid…UniqueFactorizationMonoid.prod_normalizedFactors · cited by 23UniqueFactorizationMonoid…UniqueFactorizationMonoid.dvd_of_mem_normalizedFactors · cited by 20UniqueFactorizationMonoid…UniqueFactorizationMonoid.irreducible_of_normalized_factor · cited by 15UniqueFactorizationMonoid…UniqueFactorizationMonoid.emultiplicity_eq_count_normalizedFactors · cited by 14UniqueFactorizationMonoid…UniqueFactorizationMonoid.normalizedFactors_zero · cited by 14UniqueFactorizationMonoid…UniqueFactorizationMonoid.dvd_iff_normalizedFactors_le_normalizedFactors · cited by 11UniqueFactorizationMonoid…UniqueFactorizationMonoid.normalizedFactors_mul · cited by 11UniqueFactorizationMonoid…UniqueFactorizationMonoid.normalizedFactors_irreducible · cited by 10UniqueFactorizationMonoid…RingOfIntegers.monicFactorsMod · cited by 10RingOfIntegers.monicFacto…UniqueFactorizationMonoid.normalize_normalized_factor · cited by 9UniqueFactorizationMonoid…factorization · cited by 9factorizationUniqueFactorizationMonoid.exists_mem_normalizedFactors_of_dvd · cited by 8UniqueFactorizationMonoid…UniqueFactorizationMonoid.normalizedFactors_one · cited by 8UniqueFactorizationMonoid…Multiset · cited by 2627MultisetCommMonoidWithZero · cited by 913CommMonoidWithZeroMultiset.map · cited by 876Multiset.mapUniqueFactorizationMonoid · cited by 279UniqueFactorizationMonoidNormalizationMonoid · cited by 165NormalizationMonoidnormalize · cited by 137normalizeUniqueFactorizationMonoid.factors · cited by 55UniqueFactorizationMonoid…UniqueFactorizationMonoid.nor…CITED BYCITES

Cites7

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

Cited by162

Results whose statement or proof uses this declaration.