W-closed submodule and related concepts

الملخص EN

Let R be a commutative ring with identity, and M be a left untial module.

In this paper we introduce and study the concept w-closed submodules, that is stronger form of the concept of closed submodules, where asubmodule K of a module M is called w-closed in M, "if it has no proper weak essential extension in M", that is if there exists a submodule L of M with K is weak essential submodule of L then K=L.

Some basic properties, examples of w-closed submodules are investigated, and some relationships between w-closed submodules and other related modules are studied.

Furthermore, modules with chain condition on w-closed submodules are studied.