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.
Keywords
Maximal submodules, S-maximal submodules, Almost maximal submodules, Semimaximal submodules, Semi essential submodules and Jacobson radical of modules.
Article Type
Article
How to Cite this Article
Ahmed, Muna A. and Dakheel, Shireen O.
(2015)
"S-maximal Submodules,"
Baghdad Science Journal: Vol. 12:
Iss.
1, Article 21.
DOI: https://doi.org/10.21123/bsj.2015.12.1.210-220