Generalizations of a result of Nunke (Q1611376)

The author considers Łoś's well-known definition of slender \(R\)-modules and Nunke's characterization of slender Abelian groups. He establishes results about splittings of homomorphisms between products of \(R\)-modules over general rings \(R\) with \(1\). The results are interesting variations of Nunke's important theorem showing that a subgroup \(K\) of the Baer-Specker group \(\mathbb{Z}^\mathbb{N}\) splits if the quotient is torsion-less.