Endomorphism rings and direct sums of torsion free abelian groups

Abstract

Properties of abelian groups related to a given finite rank torsion free abelian group <italic>A</italic> are analyzed in terms of End (<italic>A</italic>), the endomorphism ring of <italic>A</italic>. This point of view gives rise to generalizations of some classical theorems by R. Baer and examples of pathological direct sum decompositions of finite rank torsion free abelian groups.