Theorems · Theorem · commutative algebra
UniqueFactorizationMonoid.radical_pow
∀ {M : Type u_1} [inst : CommMonoidWithZero M] [inst_1 : NormalizationMonoid M] [inst_2 : UniqueFactorizationMonoid M]
(a : M) {n : ℕ}, n ≠ 0 → UniqueFactorizationMonoid.radical (a ^ n) = UniqueFactorizationMonoid.radical a- Defined in
- Mathlib.RingTheory.Radical.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finset.prodproof · cited by 2,356
- CommMonoidWithZerostatement and proof · cited by 913
- Finset.prod_congrproof · cited by 646
- UniqueFactorizationMonoidstatement and proof · cited by 279
- NormalizationMonoidstatement and proof · cited by 165
- UniqueFactorizationMonoid.radicalstatement · cited by 64
- UniqueFactorizationMonoid.primeFactorsproof · cited by 32
- UniqueFactorizationMonoid.primeFactors_powproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- UniqueFactorizationMonoid.exists_dvd_pow_iff_radical_dvdproof · cited by 1
- UniqueFactorizationMonoid.radical_pow_of_primeproof · cited by 1
- UniqueFactorizationMonoid.radical_pow_dvdproof · cited by 0