Exercise 10, § 1

(a) Give an example of a $\mathbf{Z}$-module M such that $\operatorname{Ass}(\operatorname{Hom}_{\mathbf{Z}}(M, M))$ is not contained in $\operatorname{Supp}(M)$ (cf. Chapter II, § 4, Exercise 24 (c)).

(b) Give an example of $\mathbf{Z}$-modules E, F such that

but $\operatorname{Ass}(F) \cap \operatorname{Supp}(E) \neq \varnothing$ (take $F = \mathbf{Z}$).