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S-maximal Submodules | ||
| Baghdad Science Journal | ||
| Article 1, Volume 12, Issue 1, 2015, Pages 210-220 | ||
| Authors | ||
| Shireen O. Dakheel; Muna A. Ahmed | ||
| 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; maximal submodules; Almost maximal submodules; Semimaximal submodules; Semi essential submodules and Jacobson radical of modules | ||
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