  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.
