Can someone point me to a reference with the proof of the following theorem?
If $R$ is a ring and $M$ is an artinian $R$-module, then there is a finite collection $\{J_1,\ldots,J_n\}$ of distinct maximal ideals of $R$ such that $M=M[J_1]\oplus \cdots \oplus M[J_n]$, where $M[J_i]=\{m\in M| J^k_im=\{0\}\text{ for some positive integer }k\}$