On Closed Dual Rickart Modules

Abstract

The notion of dual Rickart modules has been studied lately. In this article, we continue investigate and study several properties of closed dual Rickart modules which explain by Ghawi Th.Y. as a proper generalization the idea of the dual Rickart modules and as a dual concept of closed Rickart modules. A right R-module M is called closed dual Rickart if, for each , is a closed sub module of M . For a module M, we verify that M is closed dual Rickart and closed simple if and only if M is coquasi-Dedekind and Extending . We also establish that if, and are closed simple modules such that is closed dual Rickart and is projective, then either or ". Furthermore, "we give a counter example to show that the direct sums of modules is not closed under closed dual Rickart"."We also give a necessity station for a finite direct sum of closed dual Rickart modules to be closed dual Rickart". Other results are provided in this work. Examples to illustrate some results and converses are given