Our main goal in this research is to find the conditions which make
the a - small submodules are equivalent with small submodules and
so s- large submodules with large submodules, then find the relatio
-nship between the radical of module and the a - small submodules.
The objective of this paper is to continue our study for a right 1 I - rings and
to generalize the concept of 1 I - rings to modules. We call a ring R a right
1 I - ring if every right annihilator for any element of R contains a nonzero
idempotent
.