Theorems · Theorem · commutative algebra

Associates.eq_factors_of_eq_counts

∀ {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 b : Associates α},
  a ≠ 0 → b ≠ 0 → (∀ (p : Associates α), Irreducible p → p.count a.factors = p.count b.factors) → a.factors = b.factors

Defined in

Mathlib.RingTheory.UniqueFactorizationDomain.FactorSet

Cited by

1 results in Mathlib

Foundations

Depth 52 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommMonoidWithZeroUniqueFactorizationMonoidDecidableEqDecidable