In this paper, we use  the definition of the action on the set of semi-group of the structure of this research .We introduce the concepts of  -system which is a triple , ,  such that  is a Hausdorff compact space called  phase space,  is a semi-group of transformations with a continuous action  of   on  . We study and proof some theoretical properties related with that system. We also introduce the concept of Enfolding semi-group ( , ,and we prove that it is a compact right topological semi-group. In addition, we study the left and right ideals in the Enfolding semi-group. By using the dynamical system, we reflect various properties concerning with its structure for the Enfolding semi-group. Furthermore, we describe

        The purpose of this paper is to give the definition of projective 3-space PG(3,q) over Galois field GF(q), q = p^m for some prime number p and some integer m.

        Also, the definition of the plane in PG(3,q) is given and state the principle of duality.

        Moreover some theorems in PG(3,q) are proved.

     Suppose that F is a reciprocal ring which has a unity and suppose that H is an F-module. We topologize La-Prim(H), the set of all primary La-submodules of H , similar to that for FPrim(F), the spectrum of fuzzy primary ideals of F, and examine the characteristics of this topological space. Particularly, we will research the relation between La-Prim(H) and La-Prim(F/ Ann(H)) and get some results.

In this essay, we utilize m - space to specify m_X-N-connected, m_X-N-hyper connected and m_X-N-locally connected spaces and some functions by exploiting the intelligible m_X-N-open set. Some instances and outcomes have been granted to boost our tasks.

In this paper we introduce a new class of operators on Hilbert space. We
call the operators in this class, n,m- powers operators. We study this class
of operators and give some of their basic properties.

The purpose of this paper is to introduce and study the concepts of fuzzy generalized open sets, fuzzy generalized closed sets, generalized continuous fuzzy proper functions and prove results about these concepts.

Let  be a commutative ring with 1 and  be left unitary  . In this papers we introduced and studied concept P-small compressible  (An     is said to be P-small compressible if  can be embedded in every of it is nonzero P-small submodule of . Equivalently,  is P-small compressible if there exists a monomorphism  , ,     is said to be P-small retractable if  , for every non-zero P-small submodule of . Equivalently,  is P-small retractable if there exists a homomorphism  whenever  as a generalization of compressible  and retractable  respectively and give some of their advantages characterizations and examples.

Throughout this paper R represents commutative ring with identity, and M is a unitary left R-module. The purpose of this paper is to study a new concept, (up to our knowledge), named a semi-extending modules, as generalization of extending modules, where an Rmodule M is called semi-extending if every sub module of M is a semi-essential in a direct summand of M. Various properties of semi-extending module are considered. Moreover, we investigate the relationships between semi-extending modules and other related concepts, such as CLS-modules and FI- extending modules.

The main purpose of this paper is to investigate some results. When h is  -( ,δ) – Derivation on prime Γ-near-ring G and K is a nonzero semi-group ideal of G, then G is commutative .