Theorems · Theorem · commutative algebra
Irreducible.normalizedFactors_pow
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : NormalizationMonoid α] [inst_2 : UniqueFactorizationMonoid α]
{p : α},
Irreducible p → ∀ (k : ℕ), UniqueFactorizationMonoid.normalizedFactors (p ^ k) = Multiset.replicate k (normalize p)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Multisetstatement and proof · cited by 2,627
- CommMonoidWithZerostatement and proof · cited by 913
- Irreduciblestatement and proof · cited by 496
- UniqueFactorizationMonoidstatement and proof · cited by 279
- NormalizationMonoidstatement and proof · cited by 165
- UniqueFactorizationMonoid.normalizedFactorsstatement · cited by 151
- normalizestatement and proof · cited by 137
- Multiset.replicatestatement and proof · cited by 88
- UniqueFactorizationMonoid.normalizedFactors_irreducibleproof · cited by 10
- UniqueFactorizationMonoid.normalizedFactors_powproof · cited by 8
- Multiset.nsmul_singletonproof · cited by 7
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