I am attempting to count automorphisms of a particular class of finitely generated modules over rings given by $(\mathbb{Z}/p^r\mathbb{Z})[x]/(f^{n}(x))$ $(r,n\geq 1)$, where $f$ is some irreducible polynomial over $(\mathbb{Z}/p^r\mathbb{Z})[x]$. To do so, I would like to know if there is any sort of nice decomposition into cyclic submodules.
I have a hunch that something along these lines exists: if we replace $(\mathbb{Z}/p^r\mathbb{Z})$ with a finite field $K$ then the projection from $K[x]$ to $K[x]/(f^{n}(x))$ gives $K[x]/(f^{n}(x))$ the structure of a $K[x]$ module. This is a PID and hence one may apply the usual structure theorem to get a decomposition, and then go back to the $K[x]/(f^{n}(x))$ structure. This does not work for $(\mathbb{Z}/p^r\mathbb{Z})[x]$ since it is not PID.