Theorems · Theorem · commutative algebra
Associates.factors_one
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : UniqueFactorizationMonoid α] [Nontrivial α],
Associates.factors 1 = 0- Cited by
- 6 results in Mathlib
- Foundations
- Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Multisetstatement · cited by 2,627
- Nontrivialstatement and proof · cited by 2,416
- CommMonoidWithZerostatement and proof · cited by 913
- Irreduciblestatement · cited by 496
- UniqueFactorizationMonoidstatement and proof · cited by 279
- Associatesstatement and proof · cited by 210
- Associates.factorsstatement · cited by 97
- Associates.FactorSetstatement · cited by 52
- Associates.FactorSet.prodproof · cited by 20
- Multiset.prod_zeroproof · cited by 9
- Associates.factors_prodproof · cited by 9
- Associates.FactorSet.uniqueproof · cited by 5
Cited by6
Results whose statement or proof uses this declaration.
- Associates.count_powproof · cited by 3
- FractionalIdeal.count_selfproof · cited by 3
- FractionalIdeal.count_maximal_coprimeproof · cited by 2
- Associates.pow_factorsproof · cited by 1
- FractionalIdeal.count_coeproof · cited by 1
- IsDedekindDomain.HeightOneSpectrum.intValuation.map_one'proof · cited by 0