Modules with Chain Conditions on S-Closed Submodules - Mohammed, Rana Noori Majeed (Ibn AL-Haitham Journal For Pure and Applied Sciences, 2017)
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 â‰¤sc W, if D has   no  proper s- essential extension in W, that is , whenever D â‰¤ W such that D â‰¤se Hâ‰¤ 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.