A note on a theorem of Hill

Phillip Alan Griffith

Vol. 29 (1969), No. 2, 279–284

DOI: 10.2140/pjm.1969.29.279

Abstract

Recently Hill has shown the existence of an abelian p-group with the property that each infinite subgroup can be embedded in a direct summand of the same cardinality but the group is not a direct sum of countable groups. Megibben has since observed that this phenomenon occurs in a larger class of abelian groups. In this note we show that such pathology is present in modules for a rather wide class of rings. In fact, the lack of such phenomena for a particular class of modules serves as a characterization for left perfect rings. Our results also yield some facts concerning pure injective modules.

Mathematical Subject Classification

Primary: 16.40

Milestones

Received: 29 April 1968

Published: 1 May 1969