On cofinitely Rad-supplemented modules

Türkmen E., Pancar A.

International Journal of Pure and Applied Mathematics, vol.53, no.2, pp.153-162, 2009 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 53 Issue: 2
  • Publication Date: 2009
  • Journal Name: International Journal of Pure and Applied Mathematics
  • Journal Indexes: Scopus
  • Page Numbers: pp.153-162
  • Keywords: Amply) cofinitely radsupplemented module, Cofinite submodule, Generalized projective cover, Rad-supplement, (
  • Ondokuz Mayıs University Affiliated: No

Abstract

Let R be a ring and M be a left R-module. In this work some properties of (amply) cofinitely Rad-supplemented modules are developed. It is shown that if M contains a nonzero semi-hollow submodule then M is cofinitely Rad-supplemented if and only if M/N is cofinitely Rad-supplemented. Morever a module M with small radical is cofinitely Rad-supplemented such that Rad-supplements are supplements in M, then M is cofinitely supplemented. In addition, a ring R is left Rad-supplemented if and only if every left R-module is amply cofinitely Rad-supplemented. Also, we give a characterization of generalized semiperfect modules. © 2009 Academic Publications.