On Rickart Modules

Abstract

We investigate some properties of Rickart modules defined by Rizvi and Roman. Let R be an arbitrary ring with identity and M be a right R-module with S = EndR(M). A module M is called to be Rickart if for any f 2 S, rM(f) = Se, for some e2 = e 2 S. We prove that some results of principally projective rings and Baer modules can be extended to Rickart modules for this general settings.