Let $A$ be a noetherian local ring and $M$ be an artinian and noetherian module over $A$.
Does one know a priori anything about the structure of $M$?
Furthermore: if one knows that the length of $M$ as $A$-module is $1$, i.e. $M$ is simple over $A$, can one conclude that $M$ is isomorphic to $A/\mathcal m$, where $\mathcal m$ is the maximal ideal of $A$?