Theorems · Theorem · commutative algebra
isGCDMonoid_iff_exists_lcm
∀ {α : Type u_2} [inst : CommMonoidWithZero α],
IsGCDMonoid α ↔ IsCancelMulZero α ∧ ∀ (a b : α), ∃ c, ∀ (d : α), a ∣ d ∧ b ∣ d ↔ c ∣ d- Defined in
- Mathlib.Algebra.GCDMonoid.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommMonoidWithZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommMonoidWithZerostatement and proof · cited by 913
- IsCancelMulZerostatement and proof · cited by 177
- GCDMonoidproof · cited by 96
- GCDMonoid.lcmproof · cited by 78
- IsGCDMonoidstatement and proof · cited by 12
- lcm_dvd_iffproof · cited by 6
- gcdMonoidOfExistsLCMproof · cited by 1
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