On (Cofinitely) Generalized Amply Weak Supplemented Modules

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.