Goldie Pure Rickart Modules and Duality

Ghaleb Ahmed

Abstract: Let R be a commutative ring with identity and M be an R-module. Let Z2 (M) be the second singular submodule of M. In this research we introduce the concept of Goldie Pure Rickart modules and dual Goldie Pure Rickart modules as a generalization of Goldie Rickart modules and dual Goldie Rickart modules respectively. An R-module M is called Goldie Pure Rickart if f^ (-1) (Z2 (M)) is a pure ( in sense of Anderson and Fuller) submodule of M for every f EndR (M). An R-module M is called dual Goldie Pure Rickart if ^ (-1) ( Im (f)) is a pure ( in sense of Anderson and Fuller) submodule of M for every f EndR (M). Various properties of this class of modules are given and some relationships between these modules and other related modules are studied.

Keywords: Goldie Pure Rickart modules, Pure Rickart modules, dual Goldie Pure Rickart modules, dual Pure Rickart modules, Pure Submodules

How to Cite?: Ghaleb Ahmed, "Goldie Pure Rickart Modules and Duality", Volume 6 Issue 2, February 2017, International Journal of Science and Research (IJSR), Pages: 917-921, https://www.ijsr.net/getabstract.php?paperid=ART2017764, DOI: https://dx.doi.org/10.21275/ART2017764