Fethi Callialp
Department of Mathematics, University of D05us, Acibadem Department of Mathematics, University of Marmara
G�ztepe, �stanbul, Turkey
Unsal Tekir
Department of Mathematics, University of D05us, Acibadem Department of Mathematics, University of Marmara
G�ztepe, �stanbul, Turkey
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, m ∈ M and rRm ⊂ N, then m ∈ N or rM ⊂ N . 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
DOI: 10.3923/jas.2002.1016.1017
URL: https://scialert.net/abstract/?doi=jas.2002.1016.1017