nLab GCD domain

Definition

Definition

A GCD ring $R$ is a GCD domain if $R$ is also an integral domain.

Properties

Every GCD domain of dimension at most 1 is a Bézout domain.

Examples

• The ring of integers $\mathbb{Z}$

• For any GCD domain $R$, the polynomial ring $R[x]$ on one generator

• The ring of entire holomorphic functions on the complex plane

See also

• GCD ring

• integral domain

• Bézout domain

• unique factorization domain

• Euclidean domain

• field

References

• Henri Lombardi, Claude Quitté (2010): Commutative algebra: Constructive methods (Finite projective modules) Translated by Tania K. Roblo, Springer (2015) (doi:10.1007/978-94-017-9944-7, pdf)