On radicals and products

Abstract

An Abelian group G is called cotorsion-free if 0 is the only pure-injective subgroup contained in G. If G is a cotorsion-free Abelian group, we construct a slender, fr^-free Abelian group A such that Hom(, G) = 0. This will be used to answer some questions about radicals and torsion theories of Abelian groups.