Let $A$ be a Containment-Division Ring $(\operatorname{CDR})$, i.e., an integral domain that satisfies that for all $I,J$ ideals of $A$ such that $I\subseteq J$, then $I=JK$ for some ideal $K$, that is, $J\mid I$. In some algebra textbooks it is proven that 'being a Dedekind domain' and 'being CDR and noetherian' are equivalent statements.
Can someone give me an example of a CDR which is not a Dedekind domain?
Thanks in advance.