circle plus-cofinitely supplemented modules

Calisici H., Pancar A.

CZECHOSLOVAK MATHEMATICAL JOURNAL, vol.54, no.4, pp.1083-1088, 2004 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 54 Issue: 4
  • Publication Date: 2004
  • Doi Number: 10.1007/s10587-004-6453-1
  • Journal Name: CZECHOSLOVAK MATHEMATICAL JOURNAL
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1083-1088
  • Keywords: cofinite submodule, circle plus-cofinitely supplemented module, RINGS
  • Ondokuz Mayıs University Affiliated: No

Abstract

Let R be a ring and M a right R-module. M is called circle plus-cofinitely supplemented if every submodule N of M with M/N finitely generated has a supplement that is a direct summand of M. In this paper various properties of the circle plus-cofinitely supplemented modules are given. It is shown that (1) Arbitrary direct sum of circle plus-cofinitely supplemented modules is circle plus-cofinitely supplemented. (2) A ring R is semiperfect if and only if every free R-module is circle plus-cofinitely supplemented. In addition, if M has the summand sum property, then M is circle plus-cofinitely supplemented iff every maximal submodule has a supplement that is a direct summand of M.