Theorems · Definition · commutative algebra
IsBezout.toGCDDomain
(R : Type u) → [inst : CommRing R] → [IsBezout R] → [IsCancelMulZero R] → [DecidableEq R] → GCDMonoid R
Any Bézout domain is a GCD domain. This is not an instance since GCDMonoid contains data,
and this might not be how we would like to construct it.
- Defined in
- Mathlib.RingTheory.PrincipalIdealDomain
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- IsCancelMulZerostatement and proof · cited by 177
- GCDMonoidstatement · cited by 96
- IsBezoutstatement and proof · cited by 23
- IsBezout.gcdproof · cited by 12
- gcdMonoidOfGCDproof · cited by 0
Cited by1
Results whose statement or proof uses this declaration.
- exists_associated_pow_of_mul_eq_pow'proof · cited by 2