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Nearly Maximal Submodules | ||
| basrah journal of science | ||
| Article 1, Volume 34, Issue 2, 2016, Pages 1-6 PDF (0 K) | ||
| Author | ||
| Muna A. Ahmed | ||
| Abstract | ||
| In this paper we introduce the concept of nearly maximal submodules as a generalization of the class of maximal submodules, where a proper submodule N of M is called nearly maximal, if whenever a submodule W of M containing N properly implies that W+J(M)=M. Various properties of nearly maximal submodules are considered. Also we define an NM-module, which is a module in which every proper nonzero submodule is nearly maximal; we study some properties of this class of modules | ||
| Keywords | ||
| Maximal submodules; Almost maximal submodules; Nearly maximal submodules; Nearly Jacobson radical of modules; Semimaximal submodules | ||
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