Modules with chain conditions on S-closed submodules

الملخص EN

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 <* W.

if D has no proper s- essential extension in W.

that is .

whenever D < W such that D

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.