Theorems · Theorem · commutative algebra

Associates.is_pow_of_dvd_count

∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : UniqueFactorizationMonoid α]
  [inst_2 : DecidableEq (Associates α)] [inst_3 : (p : Associates α) → Decidable (Irreducible p)] {a : Associates α},
  a ≠ 0 → ∀ {k : ℕ}, (∀ (p : Associates α), Irreducible p → k ∣ p.count a.factors) → ∃ b, a = b ^ k

Defined in

Mathlib.RingTheory.UniqueFactorizationDomain.FactorSet

Cited by

1 results in Mathlib

Foundations

Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommMonoidWithZeroUniqueFactorizationMonoidDecidableEqDecidable