Vol. 56, No. 1, 1975

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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

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
Received: 14 November 1973
Revised: 4 December 1973
Published: 1 January 1975
David Marion Arnold
Charles Estep Murley