Theorems · Theorem · commutative algebra
UniqueFactorizationMonoid.normalizedFactors_prod_of_prime
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : NormalizationMonoid α] [inst_2 : UniqueFactorizationMonoid α]
[Subsingleton αˣ] {m : Multiset α}, (∀ p ∈ m, Prime p) → UniqueFactorizationMonoid.normalizedFactors m.prod = m- Cited by
- 2 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Unitsstatement and proof · cited by 2,804
- Multisetstatement and proof · cited by 2,627
- Nontrivialproof · cited by 2,416
- CommMonoidWithZerostatement and proof · cited by 913
- Multiset.prodstatement and proof · cited by 528
- UniqueFactorizationMonoidstatement and proof · cited by 279
- Primestatement and proof · cited by 277
- NormalizationMonoidstatement and proof · cited by 165
- subsingleton_or_nontrivialproof · cited by 161
- UniqueFactorizationMonoid.normalizedFactorsstatement and proof · cited by 151
- Multiset.Relproof · cited by 47
- UniqueFactorizationMonoid.prime_of_normalized_factorproof · cited by 23
Cited by2
Results whose statement or proof uses this declaration.
- UniqueFactorizationMonoid.normalizedFactors_prod_eq_self_of_subsetproof · cited by 1
- Ideal.factors_span_eqproof · cited by 0