IJPAM: Volume 19, No. 1 (2005)

ON PRIME $\Gamma M-$SUBMODULES OF $\Gamma M-$MODULES

Ünsal Tekir$^1$, Ugur Sengül$^2$
$^{1,2}$Department of Mathematics
University of Marmara
Ziverbey, Göztepe, Istanbul, TURKEY
$^1$e-mail: utekir@marmara.edu.tr
$^2$e-mail: usengul@marmara.edu.tr


Abstract.Let $G$ be a $\Gamma M$-module. A $\Gamma M$-submodule $N$ of $G$ is said to be prime if for any ideal $I$ of $M$ and for any $\Gamma M$-submodule $V$ of $G,$ $V\Gamma I\subseteq N$ implies $V\subseteq N$ or $I\subseteq\left( N:G\right) _{M}.$ The purpose of this paper is to introduce interesting properties of prime $\Gamma M$-submodules of $\Gamma M$-modules.

Received: February 4, 2005

AMS Subject Classification: 16A78

Key Words and Phrases: $\Gamma$ rings, $\Gamma M$-modules, prime $\Gamma M$-submodules

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 19
Issue: 1