Gangyong Lee, S.Tariq Rizvi, and Cosmin S.Roman studied Rickart modules. The main purpose of this paper is to develop the properties of Rickart modules . We prove that each injective and prime module is a Rickart module. And we give characterizations of some kind of rings in term of Rickart modules.

In a previous work, Ali and Ghawi studied closed Rickart modules. The main purpose of this paper is to define and study the properties of y-closed Rickart modules .We prove that, Let  and   be two -modules such that  is singular. Then  is -y-closed Rickart module if and only if   Also, we study the direct sum  of  y-closed Rickart modules.

In this paper, we develop the work of Ghawi on close dual Rickart modules and discuss y-closed dual Rickart modules with some properties. Then, we prove that, if are y-closed simple -modues and if -y-closed is a dual Rickart module, then either Hom ( ) =0 or . Also, we study the direct sum of y-closed dual Rickart modules.

Gangyong Lee, S. Tariq Rizvi, and Cosmin S. Roman studied Dual Rickart modules. The main purpose of this paper is to develop the properties Dual Rickart modules. We prove that a module M and indecomposable N if M is N-dual Rickart module, then either Hom(M, N) = 0 or every non zero R-homomorphism from M to N is a epimorphism. And we give various characterizations of some kind of rings in term of dual Rickart modules.