Exercise 16, § 2

In a ring A let p be a non-maximal prime ideal and q a p-primary ideal distinct from p. Let x be an element of $p - q$ and y an element of $A - p$ such that $p + Ay \neq A$. Show that the ideal $a = q + Axy$, such that $p \supset a \supset q$, is not primary (note that $x \in a$ is impossible).