Factorization in the self-idealization of a PID

Gyu Whan Chang, Daniel Smertnig

Let $D$ be a principal ideal domain and $R(D)=\{\left(\begin{array}{ccc}a& b0& a\end{array}\right)\mid a,b\in D\}$ be its self-idealization. It is known that $R(D)$ is a commutative no…