Theorems · Theorem · commutative algebra
UniqueFactorizationMonoid.normalizedFactors_pow
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : NormalizationMonoid α] [inst_2 : UniqueFactorizationMonoid α]
{x : α} (n : ℕ),
UniqueFactorizationMonoid.normalizedFactors (x ^ n) = n • UniqueFactorizationMonoid.normalizedFactors x- Cited by
- 8 results in Mathlib
- Foundations
- Depth 55 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.
- Multisetstatement and proof · cited by 2,627
- pow_zeroproof · cited by 1,094
- CommMonoidWithZerostatement and proof · cited by 913
- MonoidWithZeroproof · cited by 456
- zero_powproof · cited by 361
- UniqueFactorizationMonoidstatement and proof · cited by 279
- pow_succ'proof · cited by 228
- pow_ne_zeroproof · cited by 208
- NormalizationMonoidstatement and proof · cited by 165
- UniqueFactorizationMonoid.normalizedFactorsstatement and proof · cited by 151
- zero_nsmulproof · cited by 137
- nsmul_zeroproof · cited by 73
Cited by8
Results whose statement or proof uses this declaration.
- Ideal.IsDedekindDomain.ramificationIdx'_eq_normalizedFactors_countproof · cited by 5
- Ideal.ramificationIdx'_algebra_towerproof · cited by 2
- UniqueFactorizationMonoid.primeFactors_powproof · cited by 2
- UniqueFactorizationMonoid.normalizedFactors_of_irreducible_powproof · cited by 2
- UniqueFactorizationMonoid.exists_dvd_pow_iff_radical_dvdproof · cited by 1
- Ideal.eq_prime_pow_of_succ_lt_of_leproof · cited by 1
- factorization_powproof · cited by 0
- Irreducible.normalizedFactors_powproof · cited by 0