S-maximal Submodules

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...

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Bibliographic Details
Main Author: Baghdad Science Journal
Format: Article
Language:English
Published: University of Baghdad, College of Science for Women 2015-03-01
Series:مجلة بغداد للعلوم
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Online Access:http://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/542
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Summary: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. .
ISSN:2078-8665
2411-7986