International Journal of Science and Research (IJSR)

International Journal of Science and Research (IJSR)
Open Access | Fully Refereed | Peer Reviewed

ISSN: 2319-7064


Downloads: 138

Research Paper | Mathematics | Iraq | Volume 6 Issue 2, February 2017


Dual Pure Rickart Modules and Their Generalization

Ghaleb Ahmed


Abstract: Let R be a commutative ring with identity and M be an R-module. In this paper we introduce the dual concepts of Pure Rickart modules and Pure -Rickart modules as a generalization of dual Rickart modules and dual -Rickart modules respectively. Further, dual Pure Rickart modules and dual Pure -Rickart modules can be considered as a generalization of regular rings and -regular rings respectively. Furthermore, dual Pure -Rickart modules is a generalization of Pure Rickart modules. An R-module M is called dual Pure Rickart if for every f EndR (M), Im f is a pure (in sense of Anderson and Fuller) submodule of M. An R-module M is called dual Pure - Rickart if for every f EndR (M), there exist a positive integer n such that Im f^n is a pure (in sense of Anderson and Fuller) submodule of M. We show that several results of dual Rickart modules and dual -Rickart modules can be extended to dual Pure Rickart modules and dual Pure -Rickart modules for this general settings. Many results about these concepts are given and some relationships between these modules and other related modules are investigated.


Keywords: dual Pure Rickart modules, dual Pure -Rickart modules, regular modules, Pure submodules, relatively dual Rickart modules


Edition: Volume 6 Issue 2, February 2017,


Pages: 882 - 886


How to Cite this Article?

Ghaleb Ahmed, "Dual Pure Rickart Modules and Their Generalization", International Journal of Science and Research (IJSR), https://www.ijsr.net/get_abstract.php?paper_id=ART2017663, Volume 6 Issue 2, February 2017, 882 - 886

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