On a generalization of semisimple modules

Let R be a ring with identity. A module (M_R) is called an r-semisimple module if for any right ideal I of R, MI is a direct summand of (M_R) which is a generalization of semisimple and second modules. We investigate when an r-semisimple ring is semisimple and prove that a ring R with the number of nonzero proper ideals (le )4 and (J(R)=0) is r-semisimple. Moreover, we prove that R is an r-semisimple ring if and only if it is a direct sum of simple rings and we investigate the structure of module whenever R is an r-semisimple ring.