Exercise 8, § 1

Let A be a Noetherian ring, a an ideal of A, M a finitely generated A-module and P the submodule of M consisting of the $x \in M$ such that $ax = 0$. Show that $\operatorname{Ass}(M/P) \subset \operatorname{Ass}(M)$ (note that for all $x \in M$ the annihilator of $(Ax + P)/P$ is also that of $ax$ and use Exercise 7 (a)).