 Bézout domain

A Bézout domain is an integral domain in which every finitely generated ideal is principal. Equivalently, every pair $a,b$ has a greatest common divisor $d$ satisfying a Bézout identity $d=ra+sb$. A Noetherian Bézout domain is a principal ideal domain because all its ideals are finitely generated.

A Bézout domain is a specific type of integral domain in abstract algebra that possesses a particular property related to the linear combinations of its elements.