The purpose of this paper is to introduce a new type of compact spaces, namely semi-p-compact spaces which are stronger than compact spaces; we give properties and characterizations of semi-p-compact spaces.

Let R be a commutative ring with identity 1 and M be a unitary left R-module. A submodule N of an R-module M is said to be approximately pure submodule of an R-module, if for each ideal I of R. The main purpose of this paper is to study the properties of the following concepts: approximately pure essentialsubmodules, approximately pure closedsubmodules and relative approximately pure complement submodules. We prove that: when an R-module M is an approximately purely extending modules and N be Ap-puresubmodulein M, if M has the Ap-pure intersection property then N is Ap purely extending.

in this paper the notion of threshold relations by using resemblance relation are introduced to get a similarity relation from a resemnblance relation R

In this paper, certain types of regularity of topological spaces have been highlighted, which fall within the study of generalizations of separation axioms. One of the important axioms of separation is what is called regularity, and the spaces that have this property are not few, and the most important of these spaces are Euclidean spaces. Therefore, limiting this important concept to topology is within a narrow framework, which necessitates the use of generalized open sets to obtain more good characteristics and preserve the properties achieved in general topology. Perhaps the reader will realize through the research that our generalization preserved most of the characteristics, the most important of which is the hereditary property. Two t

To move forward on the path of goodness and peace, we must realize that, in the midst of the great diversity of cultures and forms of human life in the world, that we form one human nation, which God Almighty created to worship Him on His earth and under His heavens and to enjoy His bounties and natural resources that God Almighty has bestowed upon that nation. On one land, and it is governed by one common destiny. Every country has been endowed with a natural resource by God Almighty that distinguishes it from the other country to live in prosperity if these wealth are distributed equally among the members of the same society and societal justice is achieved. We must join together to work for the establishment of a sustainable global commu

In this paper we introduce the basic of definitions of groups for geometric figures; we describe some of geometric figures by using the properties of groups. The classification of some geometric figures by using the properties of some algebraic structures.

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.