Modules with Chain Conditions on S-Closed Submodules

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Rana Noori Majeed Mohammed


  Let L be a commutative ring with identity and let W be a unitary left L- module. A submodule D of an L- module W is called  s- closed submodule denoted by  D ≤sc W, if D has   no  proper s- essential extension in W, that is , whenever D ≤ W such that D ≤se H≤ W, then D = H. In  this  paper,  we study  modules which satisfies  the ascending chain  conditions (ACC) and descending chain conditions (DCC) on this kind of submodules.

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MOHAMMED, Rana Noori Majeed. Modules with Chain Conditions on S-Closed Submodules. Ibn AL- Haitham Journal For Pure and Applied Science, [S.l.], v. 30, n. 3, p. 227-235, dec. 2017. ISSN 2521-3407. Available at: <>. Date accessed: 16 jan. 2019. doi: