The duo module plays an important role in the module theory. Many researchers generalized this concept such as Ozcan AC, Hadi IMA and Ahmed MA. It is known that in a duo module, every submodule is fully invariant. This paper used the class of St-closed submodules to work out a module with the feature that all St-closed submodules are fully invariant. Such a module is called an Stc-duo module. This class of modules contains the duo module properly as well as the CL-duo module which was introduced by Ahmed MA. The behaviour of this new kind of module was considered and studied in detail,for instance, the hereditary property of the St-duo module was investigated, as the result; under certain conditions, every St-cl

    The main aim of this research is to present and to study several basic characteristics of the idea of FI-extending semimodules. The semimodule  is said to be an FI-extending semimodule if each fully invariant subsemimodule of  is essential in direct summand of . The behavior of the FI-extending semimodule with respect to direct summands as well as the direct sum is considered. In addition, the relationship between the singularity and FI-extending semimodule has been studied and investigated. Finally  extending propertywhich is stronger than FI extending,  that  has some results related to FI-extending and singularity is also investigated.

 Let R be a commutative ring with unity, let M be a left R-module. In this paper we introduce the concept small monoform module as a generalization of monoform module. A module M is called small monoform if for each non zero submodule N of M and for each   f ∈ Hom(N,M), f ≠ 0 implies ker f is small submodule in N. We give the fundamental properties of small monoform modules. Also we present some relationships between small monoform modules and some related modules

Let R be a Γ-ring and G be an R_Γ-module. A proper R_Γ-submodule S of G is said to be semiprime R_Γ-submodule if for any ideal I of a Γ-ring R and for any R_Γ-submodule A of G such that or which implies that . The purpose of this paper is to introduce interesting results of semiprime R_Γ-submodule of R_Γ-module which represents a generalization of semiprime submodules.

 Let  be a commutative ring with identity and a fixed ideal of  and  be an unitary -module.We say that a proper submodule  of  is -semi prime submodule if with . In this paper, we investigate some properties of this class of submodules. Also, some characterizations of -semiprime submodules will be given, and we show that under some assumptions -semiprime submodules and semiprime submodules are coincided.

     Ring theory is one of the influential branches of abstract algebra. In this field, many algebraic problems have been considered by mathematical researchers who are working in this field. However, some new concepts have been created and developed to present some algebraic structures with their properties. Rings with derivations have been studied fifty years ago, especially the relationships between the derivations and the structure of a ring. By using the notatin of derivation, many results have been obtained in the literature with different types of derivations. In this paper, the concept of the derivation theory of a ring has been considered. This study presented the definition of

     Ring theory is one of the influ

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.

The main purpose of this paper is to study some results concerning reduced ring with another concepts as semiprime ring ,prime ring,essential ideal ,derivations and homomorphism ,we give some results a bout that.

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.