Theorems · Theorem · commutative algebra
Associates.factors_eq_top_iff_zero
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : UniqueFactorizationMonoid α] {a : Associates α},
a.factors = ⊤ ↔ a = 0- Cited by
- 1 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.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement and proof · cited by 9,680
- Multisetstatement · cited by 2,627
- Nontrivialproof · 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 and proof · cited by 97
- Associates.FactorSetstatement · cited by 52
- Associates.factors_prodproof · cited by 9
- Associates.factors_zeroproof · cited by 7
- Associates.factors_subsingletonproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Associates.factors_eq_some_iff_ne_zeroproof · cited by 2