Exercise 7, § 2

Let $S$ be a multiplicative subset of a ring $A$; for every family $(M_t)_{t \in I}$ of $A$-modules, define a canonical homomorphism $S^{-1} \prod_{t \in I} M_t \to \prod_{t \in I} S^{-1}M_t$ of $S^{-1}A$-modules. Give an example where this homomorphism is neither injective nor surjective (cf. Exercise 3).