Pseudo Weakly Closed Submodules and Related Concepts

Main Article Content

Haibat K. Mohammadali Mohammad E. Dahash

Abstract

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.


 

Article Details

How to Cite
MOHAMMADALI, Haibat K.; DAHASH, Mohammad E.. Pseudo Weakly Closed Submodules and Related Concepts. Ibn AL- Haitham Journal For Pure and Applied Science, [S.l.], v. 33, n. 1, p. 84-95, jan. 2020. ISSN 2521-3407. Available at: <http://jih.uobaghdad.edu.iq/index.php/j/article/view/2376>. Date accessed: 25 may 2020. doi: http://dx.doi.org/10.30526/33.1.2376.
Section
mathematics