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WEAKLY PRIME SUBMODULES AND PRIME SUBMODULES

Published online by Cambridge University Press:  23 August 2006

A. AZIZI
A. AZIZI
Affiliation:
Department of Mathematics, College of Sciences, Shiraz University, Shiraz 71454, Iran e-mail: a_azizi@yahoo.com, razizi@susc.ac.ir
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Abstract

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A proper submodule $N$ of an $R$-module $M$ is called a weakly prime submodule, if for each submodule $K$ of $M$ and elements $a, b$ of $R$, $abK \subseteq N$, implies that $aK\subseteq N$ or $bK\subseteq N$. In this paper we will study weakly prime submodules and we shall compare weakly prime submodules with prime submodules.

Keywords

13C9913E05
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 48 , Issue 2 , May 2006 , pp. 343 - 346
Copyright
2006 Glasgow Mathematical Journal Trust