IJPAM: Volume 76, No. 3 (2012)
SUPPLEMENTED MODULES



Faculty of Sciences and Arts
Ondokuz Mayıs University
55139, Kurupelit-Samsun, TURKEY
Abstract. Let be a ring and
be a left
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)
is Artinian if and only if
is a
GAWS-module and satisfies DCC on generalized weak supplement submodules and
on small submodules. (2) A ring
is semilocal if and only if every left
-module is CGAWS-module.
Received: October 20, 2011
AMS Subject Classification: 16D10, 16D99, 16P70
Key Words and Phrases: cofinitely generalized weak supplemented module, generalized amply weak supplemented module, cofinitely generalized amply weak supplemented module
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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 76
Issue: 3