Exercise 3, § 1

Let $M$ be an $A$-module and $N$ a submodule of $M$. Show that every prime ideal $p \in \operatorname{Ass}(M/N)$ which does not contain $\operatorname{Ann}(N)$ is associated with $M$. Give an example of an ideal $p$ belonging to $\operatorname{Ass}(M/N)$ but not to $\operatorname{Ass}(M)$ (take $A$ to be an integral domain, $M = A$).