Exercise 14, § 1

Let A be an integral domain, $a \neq 0$ an element of A and p an element of $\operatorname{Ass}(A/aA)$. Show that, for every element b $\neq 0$ of p, $p \in \operatorname{Ass}(A/bA)$ (if c $\in A$ is such that the relation $xc \in aA$ is equivalent to $x \in p$, show that there exists d $\in A$ such that $xd \in bA$ is equivalent to $xc \in aA$).