The structure theorem for finitely generated modules over a principal ideal domain is well known. My question is about the noncommutative version of this theorem:
Let $R$ be a ring with identity without non-zero zero-divisors and such that every left ideal and every right ideal of $R$ is principal. An example of such a ring is a division ring $D$ or a polynomial ring $D[x]$ over the division ring $D$. If $M$ is a finitely generated module over $R$ is there a simple structure for $M$ as in the commutative case?