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W-Closed Submodule and Related Concepts

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.

College of Education for Pure Sciences Ibn Al-Haitham

Haibat K. Mohammad Ali Mohammad E. Dahsh

Ibn AL-Haitham Journal For Pure and Applied Sciences

2018

Title: W-Closed Submodule and Related Concepts

Description:

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.

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W-Closed Submodule and Related Concepts

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