Theorems · Theorem · commutative algebra
UniqueFactorizationMonoid.radical_pow_dvd
∀ {M : Type u_1} [inst : CommMonoidWithZero M] [inst_1 : NormalizationMonoid M] [inst_2 : UniqueFactorizationMonoid M]
{a : M} {n : ℕ}, UniqueFactorizationMonoid.radical (a ^ n) ∣ UniqueFactorizationMonoid.radical a- Defined in
- Mathlib.RingTheory.Radical.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- eq_or_neproof · cited by 1,117
- pow_zeroproof · cited by 1,094
- CommMonoidWithZerostatement and proof · cited by 913
- UniqueFactorizationMonoidstatement and proof · cited by 279
- NormalizationMonoidstatement and proof · cited by 165
- dvd_reflproof · cited by 97
- UniqueFactorizationMonoid.radicalstatement and proof · cited by 64
- UniqueFactorizationMonoid.radical.congr_simpproof · cited by 6
- UniqueFactorizationMonoid.radical_oneproof · cited by 5
- UniqueFactorizationMonoid.radical_powproof · cited by 3
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