Abelian groups, A, such that Hom(A,−−−) preserves direct sums of copies of A

David Marion Arnold and Charles Estep Murley

Vol. 56 (1975), No. 1, 7–20

DOI: 10.2140/pjm.1975.56.7

Abstract

An R-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.

Mathematical Subject Classification 2000

Primary: 20K25

Milestones

Received: 14 November 1973

Revised: 4 December 1973

Published: 1 January 1975