Mathlib Map

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
Assumes
CommRingIsBezoutIsCancelMulZeroDecidableEq

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.

Cited by1

Results whose statement or proof uses this declaration.