On (cofinitely) generalized amply weak supplemented modules

Yüzbaşi F., Eren Ş.

International Journal of Pure and Applied Mathematics, vol.76, no.3, pp.333-342, 2012 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 76 Issue: 3
  • Publication Date: 2012
  • Journal Name: International Journal of Pure and Applied Mathematics
  • Journal Indexes: Scopus
  • Page Numbers: pp.333-342
  • Keywords: Cofinitely generalized amply weak supplemented module, Cofinitely generalized weak supplemented module, Generalized amply weak supplemented module
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

Let R be a ring and M be a left R-module. In this paper, we will study some properties of (cofinitely) generalized amply weak supplemented modules (CGAWS) as a generalization of (cofinitely) amply weak supplemented and give a new characterization of semilocal rings using CGAWS-modules. Nevertheless, we will show that (1) M is Artinian if and only if M is a GAWSmodule and satisfies DCC on generalized weak supplement submodules and on small submodules. (2) A ring R is semilocal if and only if every left R-module is CGAWS-module. © 2012 Academic Publications, Ltd.