Exercise 7, § 2

Let A be a Noetherian ring, M a finitely generated A-module and $(p_i)_{1 \leq i \leq n}$ a sequence obtained by arranging the elements of $\operatorname{Ass}(M)$ in any order. Show that there exists a composition series $(M_i)_{0 \leq i \leq n}$ of $M$ such that, for $0 \leq i \leq n - 1$, $M_{i+1}$ is $p_i$-primary in $M$, (use Proposition 4 of no. 3).