MODULES WHOSE MAXIMAL SUBMODULES HAVE SUPPLEMENTS

Abstract

A ring R is semiperfect if and only if, for every (cyclic)R-module M, every maximal submodule has (ample) supplements in M. A non-local commutative domain R is h-local if and only if, for every (cyclic) torsion R-module M, every maximal submodule of M has (ample) supplements in M.

ACKNOWLEDGMENTS

This paper arose out of a visit to Dokuz Eylül University in 1998 by the third author who wishes to thank the Department of Mathematics of the Faculty of Arts and Science for their hospitality. All three authors wish to thank TUBITAK and the Science Foundation of the Faculty of Arts and Science for their financial support. The authors would like to thank the referee for a number of very helpful comments on an earlier version of this paper.