A Bézout domain is an integral domain in which every finitely generated ideal is a principal ideal. Equivalently, every ideal generated by two elements is principal (Stacks Project, Tag 0ASR).
Every principal ideal domain is a Bézout domain. A Bézout domain is a principal ideal domain iff it is Noetherian, since Noetherianity makes every ideal finitely generated.
Zhang and Qi (2026) proved that every nonzero commutative von Neumann regular ring is a principal quotient 
of a characteristic-zero
Bézout domain, with 
a nonzero nonunit and 
the Jacobson radical
of 
.
