Let M be an R-module, where R is a commutative ring with unity. A submodule N of M is called e-small (denoted by N e  M) if N + K = M, where K e  M implies K = M. We give many properties related with this type of submodules.

Let R be a commutative ring with identity and M be a unitary R- module. We shall say that M is a primary multiplication module if every primary submodule of M is a multiplication submodule of M. Some of the properties of this concept will be investigated. The main results of this paper are, for modules M and N, we have M N and HomR (M, N) are primary multiplications R-modules under certain assumptions.

Let  be a commutative ring with identity and let   be an R-module. We call an R-submodule  of  as P-essential if  for each nonzero prime submodule  of    and 0  . Also, we call an R-module  as P-uniform if every non-zero submodule  of  is P-essential. We give some properties of P-essential and introduce many properties to P-uniform R-module. Also, we give conditions under which a submodule  of a multiplication R-module  becomes P-essential. Moreover, various properties of P-essential submodules are considered.

Let R be a ring with identity and let M be a left R-module. M is called µ-lifting modulei f for every sub module A of M, There exists a direct summand D of M such that M = D D', for some sub module D' of M such that A≤D and A D'<<_µ D'. The aim of this paper is to introduce properties of µ-lifting modules. Especially, we give characterizations of µ-lifting modules. On the other hand, the notion of amply µ-supplemented iis studied as a generalization of amply supplemented modules, we show that if M is amply µ-supplemented such that every µ-supplement sub module of M

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.

The soft sets were known since 1999, and because of their wide applications and their great flexibility to solve the problems, we used these concepts to define new types of soft limit points, that we called soft turning points.Finally, we used these points to define new types of soft separation axioms and we study their properties.

The main goal of this paper is to introduce and study a new concept named d^*-supplemented which can be considered as a generalization of W- supplemented modules and d-hollow module. Also, we introduce a d^*-supplement submodule. Many relationships of d^*-supplemented modules are studied. Especially, we give characterizations of d^*-supplemented modules and relationship between this kind of modules and other kind modules for example every d-hollow (d-local) module is d^*-supplemented and by an example we show that the converse is not true.