Duality and self-reflexive torsion-free abelian groups Original Research Article

We characterize the torsion-free abelian groups G of finite rank such that Hom(−, G) defines a rank preserving duality on the category of End(G)-submodules of finite sums of copies of G. Our results provide a maximal extension of Warfieldʹs duality result for torsion-free groups of finite rank. In order to obtain our extension, we study the torsion-free abelian groups G for which G congruent withnat Hom(Hom(G, G), G).