Abelian groups,A, such thatHom(A,−−−) preserves direct sums of copies ofA

An /^-module, A, is self-small if Hom(A,-) preserves direct sums of copies of A. Various conditions on the endomorphism ring of a module which guarantee that it is self-small are studied. Various results are proved about subgroups of direct sums or direct products of copies of a self-small abelian group A, which generalize results previously known when A is torsion free of rank one.