principal ideal ring

A commutative ring $R$ in which all ideals are principal, i.e. generated by a single ring element, is called a principal ideal ring. If $R$ is also an integral domain, it is a principal ideal domain.

Some well-known principal ideal rings are the ring $\mathbb{Z}$ of integers, its factor rings $\mathbb{Z}/n\mathbb{Z}$ , and any polynomial ring over a field.