Theorems · Theorem · commutative algebra

Associates.count_mul_of_coprime

∀ {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},
  b ≠ 0 →
    ∀ {p : Associates α},
      Irreducible p →
        (∀ (d : Associates α), d ∣ a → d ∣ b → ¬Prime d) →
          p.count a.factors = 0 ∨ p.count a.factors = p.count (a * b).factors

Defined in

Mathlib.RingTheory.UniqueFactorizationDomain.FactorSet

Cited by

0 results in Mathlib

Foundations

Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommMonoidWithZeroUniqueFactorizationMonoidDecidableEqDecidable