Theorems · Theorem · commutative algebra

Associates.dvd_count_pow

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

Defined in

Mathlib.RingTheory.UniqueFactorizationDomain.FactorSet

Cited by

1 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommMonoidWithZeroUniqueFactorizationMonoidDecidableEqDecidableNontrivial