Exercise 19, § 1

Let A be the ring of a valuation of height 2, $\Gamma$ its order group, $\Gamma_1$ the unique isolated subgroup of $\Gamma$ distinct from $\{0\}$ and $\Gamma$ and $y > 0$ an element of $\Gamma$ not belonging to $\Gamma_1$. Let $a$ be the ideal of those $x \in A$ such that $v(x) \geq y$, $b$ the ideal of those $x \in A$ such that $v(x) > y$, $E = A/a$ and $F = A/b$. Show that $\operatorname{Ass}_f(\operatorname{Hom}_A(E, F))$ is distinct from $\operatorname{Ass}_f(F) \cap \operatorname{Supp}(E)$. \*