Bézout domain

Summary

A Bézout domain is an integral domain in which every finitely generated ideal is principal. In such a ring Bézout's identity holds: a gcd of $a$ and $b$ can be written as $ax + by$. Every principal ideal domain is a Bézout domain, and a Noetherian Bézout domain is a principal ideal domain. Bézout domains are GCD domains and Prüfer domains.