Let $R=\mathbb{C}[[x]]$ be the ring of formal power series and $S=M_2(R)$ be the set of all $2\times 2$ matrices of entries in $R$.
Then characterize all finitely generated left-modules on $S$ and their endomorphism rings.
I know that $R$ is a PID and also Noetherian. Is there some similar results about left-modules like the well-known 'stucture of finitely generated module over PID' ?
Thanks.