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Research Article
 

On Finite Union of Prime Submodules



Fethi Callialp and Unsal Tekir
 
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ABSTRACT

Let R be an associative ring with identify and M be a unital left R-module. A proper submodule N of M is called prime if whenever r ∈ R, mM and rRmN, then mN or rMN . In this paper we show the following two result. i) The prime avoidance theorem for unital left modules over noncommutative rings. ii) Let S be an m – system subset of a ring R and S* be an S – system subset of an R- module M. Let N be a submodule of M which is maximal in M-S*. if the ideal (N:M) is maximal is R – S, then N is a prime submodule of M.

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  How to cite this article:

Fethi Callialp and Unsal Tekir , 2002. On Finite Union of Prime Submodules. Journal of Applied Sciences, 2: 1016-1017.

DOI: 10.3923/jas.2002.1016.1017

URL: https://scialert.net/abstract/?doi=jas.2002.1016.1017

REFERENCES
1:  Lu, C.P., 1997. Unions of prime sub-modules. Houston J. Math., 23: 203-213.

2:  Lam, Y.Y., 1999. Lectures on Modules and Rings. Springer Verlag, Berlin, Heidelberg.

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