Pseudo weakly closed submodules and related concepts

Abstract EN

Let be a commutative ring with identity, and be a unitary left -module.

In this paper we introduce the concept pseudo weakly closed submodule as a generalization of -closed submodules, where a submodule of an -module is called a pseudo weakly closed submodule, if for all , there exists a -closed submodule of with is a submodule of such that .

Several basic properties, examples and results of pseudo weakly closed submodules are given.

Furthermore the behavior of pseudo weakly closed submodules in class of multiplication modules are studied.

On the other hand modules with chain conditions on pseudo weakly closed submodules are established.

Also, the relationships of pseudo weakly closed submodules with other classes of modules are discussed.