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S-maximal Submodules

Journal: Baghdad Science Journal (Vol.12, No. 1)

Publication Date:

Authors : ;

Page : 210-220

Keywords : Maximal submodules; S-maximal submodules; Almost maximal submodules; Semimaximal submodules; Semi essential submodules and Jacobson radical of modules.;

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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.

Last modified: 2015-06-20 19:40:04