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

Goldie Pure Rickart Modules and Duality

Ghaleb Ahmed ^[2]

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

Edition: Volume 6 Issue 2, February 2017,

Pages: 917 - 921

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