I'm trying to prove the next proposition:
Let $M$ be a semisimple module over a ring R. Then $L(M)\in \mathbb{N} $ if and only if $M$ is finitely generated.
Where $L(M)$ is the length of $M$, which by definition is the length of a proper composition series.
For the $ ( \Longrightarrow )$ implication I use that have finite lenght implies that the module is artinian and noetherian and since being noetherian implies finitely generated, it's done.
But I'm stuck in the $(\Longleftarrow)$ implication; Any help is appreciated, thank you.