Baer-Specker relations

Consider the Baer-Specker group $\IZ^\IN$ and choose a free abelian group $F$ with an epimorphism $\pi : F \to \IZ^\IN$ (for example, to make this example explicit, the free abelian group on the underlying set of $\IZ^\IN$). Let $K \subseteq F$ be its kernel (which is also free abelian). In this entry, we consider the inclusion $m : K \hookrightarrow F$. It provides an example of a strict monomorphism which is not regular.