A gamma T_ pure sub-module also the intersection property for gamma T_pure sub-modules have been studied in this action. Different descriptions and discuss some ownership, as Γ-module Z owns the TΓ_pure intersection property if and only if (J2 ΓK ∩ J^2  ΓF)=J^2 Γ(K ∩ F) for each Γ-ideal J and for all TΓ_pure K, and F in Z Q/P is TΓ_pure sub-module in Z/P, if P in Q.

Let  be a ring with identity and  be a submodule of a left - module . A submodule  of  is called - small in  denoted by , in case for any submodule  of ,  implies .  Submodule  of  is called semi -T- small in , denoted by , provided for submodule  of ,  implies that . We studied this concept which is a generalization of the small submodules and obtained some related results

        Let R be a commutative ring with identity, and let M be a unitary R-module. We introduce a concept of almost bounded submodules as follows: A submodule N of an R-module M is called an almost bounded submodule if there exists xÃŽM, xÏN such that ann_R(N)=ann_R(x).

        In this paper, some properties of almost bounded submodules are given. Also, various basic results about almost bounded submodules are considered.

        Moreover, some relations between almost bounded submodules and other types of modules are considered.

Let R be a commutative ring with unity and let M be a left R-module. We define a proper submodule N of M to be a weakly prime if whenever  r  R,  x  M, 0  r x  N implies  x  N  or  r  (N:M). In fact this concept is a generalization of the concept weakly  prime ideal, where a proper ideal P of R is called a weakly prime, if for all a, b  R, 0  a b  P implies a  P or b  P. Various properties of weakly prime submodules are considered. 

    Let  be a non-zero right module over a ring  with identity. The weakly second submodules is studied in this paper. A non-zero submodule  of   is weakly second Submodule when  ,  where ,  and  is a submodule of  implies either  or   . Some connections between these modules and other related modules are investigated and number of conclusions  and characterizations are gained.

     Let  be a ring with identity. Recall that a submodule  of a left -module  is called strongly essential if for any nonzero subset  of , there is  such that , i.e., . This paper introduces a class of submodules called se-closed, where a submodule  of  is called se-closed if it has no proper strongly essential extensions inside . We show by an example that the intersection of two se-closed submodules may not be se-closed. We say that a module  is have the se-Closed Intersection Property, briefly se-CIP, if the intersection of every two se-closed submodules of  is again se-closed in . Several characterizations are introduced and studied for each of these concepts. We prove for submodules  and  of  that a module  has the