Let  R  be a commutative ring  with identity  and  E  be a unitary left  R – module .We introduce  and study the concept Weak Pseudo – 2 – Absorbing submodules as  generalization of weakle – 2 – Absorbing submodules , where a proper submodule  A of  an  R – module  E is  called  Weak Pseudo – 2 – Absorbing  if   0 ≠ rsx   A   for  r, s  R , x  E , implies that  rx   A + soc ( E ) or  sx  A + soc (E)  or   rs  [ A + soc ( E ) E ]. Many basic  properties, char

Let R be a commutative ring with 1 and M be a (left) unitary R – module. This essay gives generalizations for the notions prime module and some concepts related to it. We termed an R – module M as semi-essentially prime if annR (M) = annR (N) for every non-zero semi-essential submodules N of M. Given some of their advantages characterizations and examples, and we study the relation between these and some classes of modules.

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  be a commutative ring with identity and  be an -module. In this work, we present the concept of semi--maximal sumodule as a generalization of -maximal submodule.

We present that a submodule  of an -module  is a semi--maximal (sortly --max) submodule if  is a semisimple -module (where  is a submodule of ). We  investegate some properties of these kinds of modules.

      Fuchs introduced purely extending modules as a generalization of extending modules. Ahmed and Abbas gave another generalization for extending modules named semi-extending modules. In this paper, two generalizations of the extending modules are combined to give another generalization. This generalization is said to be almost semi-extending. In fact, the purely extending modules lies between the extending and almost semi-extending modules. We also show that an almost semi-extending module is a proper generalization of purely extending. In addition, various examples and important properties of this class of modules are given and considered. Another characterization of almost semi-extending modules is established. Moreover, the re