In this paper, we introduce and study a new concept (up to our knowledge) named CL-duo modules, which is bigger than that of duo modules, and smaller than weak duo module which is given by Ozcan and Harmanci. Several properties are investigated. Also we consider some characterizations of CL-duo modules. Moreover, many relationships are given for this class of modules with other related classes of modules such as weak duo modules, P-duo modules.

       A submodule N of a module M  is said to be s-essential if it has nonzero intersection with any nonzero small submodule in M. In this article, we introduce and study a class of modules in which all its nonzero endomorphisms have non-s-essential kernels, named, strongly -nonsigular. We investigate some properties of strongly -nonsigular modules. Direct summand, direct sums and some connections of such modules are discussed.        

   Let  be a right module over an arbitrary ring  with identity and  . In this work, the coclosed rickart modules as a generalization of  rickart  modules is given. We say  a module  over   coclosed rickart if for each ,   is a coclosed submodule of  . Basic results over this paper are introduced and connections between these modules and otherwise notions are investigated.

In this paper, we introduce a new concept named St-polyform modules, and show that the class of St-polyform modules is contained properly in the well-known classes; polyform, strongly essentially quasi-Dedekind and ?-nonsingular modules. Various properties of such modules are obtained. Another characterization of St-polyform module is given. An existence of St-polyform submodules in certain class of modules is considered. The relationships of St-polyform with some related concepts are investigated. Furthermore, we introduce other new classes which are; St-semisimple and ?-non St-singular modules, and we verify that the class of St-polyform modules lies between them.

    Suppose that A be an abelain ring with identity, B be a unitary (left) A-module, in this paper ,we introduce a type of modules ,namely Quasi-semiprime A-module, whenever   is a Prime Ideal For proper submodule N of  B,then B is called Quasi-semiprime module ,which is a Generalization of Quasi-Prime A-module,whenever  ann_AN is a prime ideal for proper submodule N of B,then B is Quasi-prime module .A comprchensive study of these modules is given,and we study the Relationship between quasi-semiprime module and quasi-prime .We put the codition coprime over cosemiprime ring for the two cocept quasi-prime module and quasi-semiprime module are equavelant.and the cocept of  prime module and quasi

An R-module M is called a 2-regular module if every submodule N of M is 2-pure submodule, where a submodule N of M is 2-pure in M if for every ideal I of R, I2MN = I2N, [1]. This paper is a continuation of [1]. We give some conditions to characterize this class of modules, also many relationships with other related concepts are introduced.

     The -s-extending modules will be purpose of this paper, a module M  is -s-extending if each submodule in M is essential in submodule has a supplement that is direct summand. Initially, we give relation between this concept with weakly supplement extending modules and -supplemented modules. In fact, we gives the following implications:

Lifting modules   -supplemented modules   -s-extending modules  weakly supplement extending modules.

It is also we give examples show that, the converse of this result is not true. Moreover, we study when the converse of this result is true.

There are two (non-equivalent) generalizations of Von Neuman regular rings to modules; one in the sense of Zelmanowize which is elementwise generalization, and the other in the sense of Fieldhowse. In this work, we introduced and studied the approximately regular modules, as well as many properties and characterizations are considered, also we study the relation between them by using approximately pointwise-projective modules.

Let R be a commutative ring with identity, and let M be a unity R-module. M is called a bounded R-module provided that there exists an element x?M such that annR(M) = annR(x). As a generalization of this concept, a concept of semi-bounded module has been introduced as follows: M is called a semi-bounded if there exists an element x?M such that . In this paper, some properties and characterizations of semi-bounded modules are given. Also, various basic results about semi-bounded modules are considered. Moreover, some relations between semi-bounded modules and other types of modules are considered.

he concept of small monoform module was introduced by Hadi and Marhun, where a module U is called small monoform if for each non-zero submodule V of U and for every non-zero homomorphism f ∈ Hom R (V, U), implies that ker f is small submodule of V. In this paper the author dualizes this concept; she calls it co-small monoform module. Many fundamental properties of co-small monoform module are given. Partial characterization of co-small monoform module is established. Also, the author dualizes the concept of small quasi-Dedekind modules which given by Hadi and Ghawi. She show that co-small monoform is contained properly in the class of the dual of small quasi-Dedekind modules. Furthermore, some subclasses of co-small monoform are investiga