Exercise 5, § 2

Give an example of a sequence $(P_n)$ of sub-$\mathbf{Z}$-modules of $\mathbf{Z}$ such that, for $S = \mathbf{Z}^*$, the submodule $S^{-1} \left( \bigcap_n P_n \right)$ is distinct from $\bigcap (S^{-1}P_n)$.