Theorems · Theorem · commutative algebra
lcm_eq_zero_iff
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : GCDMonoid α] (a b : α), lcm a b = 0 ↔ a = 0 ∨ b = 0- Defined in
- Mathlib.Algebra.GCDMonoid.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommMonoidWithZeroGCDMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- MulZeroClass.mul_zeroproof · cited by 2,091
- CommMonoidWithZerostatement and proof · cited by 913
- Associatedproof · cited by 296
- GCDMonoid.gcdproof · cited by 143
- GCDMonoidstatement and proof · cited by 96
- mul_eq_zeroproof · cited by 94
- Associated.symmproof · cited by 87
- GCDMonoid.lcmstatement and proof · cited by 78
- Associated.reflproof · cited by 25
- Associated.transproof · cited by 22
- associated_zero_iff_eq_zeroproof · cited by 4
- GCDMonoid.gcd_mul_lcmproof · cited by 3
Cited by0
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