A Note on Rickart Modules

We study the notion of Rickart property in a general module theoretic setting as a generalization to the concept of Baer modules and right Rickart rings. A module $M_{R}$ is called Rickart if the right annihilator in $M_{R}$ of each left principal ideal of $End_{R}(M)$ is generated by an idempotent. Characterizations of Rickart modules are given. We give sufficient conditions for direct sums of Rickart modules to be Rickart. We extend some useful results of right Rickart rings to the theory of Rickart modules.