S-maximal Submodules Muna A. Ahmed|Shireen O. Dakheel

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Baghdad Science Journal

Abstract

Throughout this paper R represents a commutative ring with identity and all R-modules M are unitary left R-modules. In this work we introduce the notion of S-maximal submodules as a generalization of the class of maximal submodules, where a proper submodule N of an R-module M is called S-maximal, if whenever W is a semi essential submodule of M with N ? W ? M, implies that W = M. Various properties of an S-maximal submodule are considered, and we investigate some relationships between S-maximal submodules and some others related concepts such as almost maximal submodules and semimaximal submodules. Also, we study the behavior of S-maximal submodules in the class of multiplication modules. Farther more we give S-Jacobson radical of rings and modules. .

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1.
Journal BS. S-maximal Submodules. BSJ [Internet]. 1Mar.2015 [cited 9Dec.2019];12(1):210-2. Available from: http://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/542
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