Theorems · Theorem · commutative algebra
Associates.prime_pow_dvd_iff_le
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : UniqueFactorizationMonoid α]
[inst_2 : DecidableEq (Associates α)] [inst_3 : (p : Associates α) → Decidable (Irreducible p)] {m p : Associates α},
m ≠ 0 → Irreducible p → ∀ {k : ℕ}, p ^ k ≤ m ↔ k ≤ p.count m.factors- Cited by
- 7 results in Mathlib
- Foundations
- Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommMonoidWithZerostatement and proof · cited by 913
- Irreduciblestatement and proof · cited by 496
- UniqueFactorizationMonoidstatement and proof · cited by 279
- Associatesstatement and proof · cited by 210
- Associates.factorsstatement and proof · cited by 97
- Associates.countstatement · cited by 79
- Associates.FactorSetproof · cited by 52
- Associates.bcountproof · cited by 6
- Associates.prime_pow_le_iff_le_bcountproof · cited by 1
Cited by7
Results whose statement or proof uses this declaration.
- Associates.count_ne_zero_iff_dvdproof · cited by 5
- IsDedekindDomain.HeightOneSpectrum.intValuation_le_pow_iff_dvdproof · cited by 5
- Ideal.count_associates_factors_eqproof · cited by 4
- Associates.le_of_count_ne_zeroproof · cited by 3
- IsDedekindDomain.HeightOneSpectrum.intValuation_exists_uniformizerproof · cited by 3
- Ideal.finprod_countproof · cited by 1
- IsDedekindDomain.HeightOneSpectrum.intValuation.map_add_le_max'proof · cited by 0