IJPAM: Volume 76, No. 3 (2012)

ON (COFINITELY) GENERALIZED AMPLY WEAK
SUPPLEMENTED MODULES

Figen Yüzbaşi$^1$, Şenol Eren$^2$
$^{1,2}$Department of Mathematics
Faculty of Sciences and Arts
Ondokuz Mayıs University
55139, Kurupelit-Samsun, TURKEY


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 GAWS-module 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.

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