Theorems · Theorem · commutative algebra
UniqueFactorizationMonoid.primeFactors_pow
∀ {M : Type u_1} [inst : CommMonoidWithZero M] [inst_1 : NormalizationMonoid M] [inst_2 : UniqueFactorizationMonoid M]
(a : M) {n : ℕ}, n ≠ 0 → UniqueFactorizationMonoid.primeFactors (a ^ n) = UniqueFactorizationMonoid.primeFactors a- Defined in
- Mathlib.RingTheory.Radical.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement · cited by 13,712
- Multisetproof · cited by 2,627
- CommMonoidWithZerostatement and proof · cited by 913
- UniqueFactorizationMonoidstatement and proof · cited by 279
- Multiset.toFinsetproof · cited by 230
- NormalizationMonoidstatement and proof · cited by 165
- UniqueFactorizationMonoid.normalizedFactorsproof · cited by 151
- UniqueFactorizationMonoid.primeFactorsstatement · cited by 32
- UniqueFactorizationMonoid.normalizedFactors_powproof · cited by 8
- Multiset.toFinset_nsmulproof · cited by 8
Cited by2
Results whose statement or proof uses this declaration.
- UniqueFactorizationMonoid.radical_powproof · cited by 3
- UniqueFactorizationMonoid.primeFactors_pow'proof · cited by 0