The main objective of this thesis is to study new concepts (up to our knowledge) which are P-rational submodules, P-polyform and fully polyform modules. We studied a special type of rational submodule, called the P-rational submodule. A submodule N of an R-module M is called P-rational (Simply, N≤_prM), if N is pure and Hom_R (M/N,E(M))=0 where E(M) is the injective hull of M. Many properties of the P-rational submodules were investigated, and various characteristics were given and discussed that are analogous to the results which are known in the concept of the rational submodule. We used a P-rational submodule to define a P-polyform module which is contained properly in the polyform module. An R-module M is called P-polyform if every es

The goal of this discussion is to study the twigged of pure-small (pr-small) sub- moduleof a module W as recirculation of a small sub-module, and we give some basic idiosyncrasy and instances of this kind of sub-module. Also, we give the acquaint of pure radical of a module W (pr-radical) with peculiarities.

        A new generalizations of coretractable modules are introduced where a module  is called t-essentially (weakly t-essentially) coretractable if for all proper submodule  of , there exists f End( ), f( )=0 and Imf _tes  (Im f + _tes ). Some basic properties are studied and many relationships between these classes and other related one are presented.

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.

In this work, we introduce the algebraic structure of semigroup with G-algebra is called GS-Algebra as extension of algebras QS-algebra and BP-algebra and then some basic properties are investigated. Several examples are presented. Also, some ideals in this concept are studied such as GS-ideal and closed-ideal. Some properties and characterizations of GS-ideal are presented. The relationships between GS-ideal and closed-ideal are studied. Furthermore, some results of GS-ideal in GS-Algebra under homomorphism are discussed. Finally, the graph (by its annihilator-ideal) as the simple graph with elements of a GS-Algebra is studied and some related properties are given. Several examples are presented and some theorems are proved.

The present study involves experimental analysis of the modified Closed Wet Cooling Tower (CWCT) based on first and second law of thermodynamics, to gain a deeper knowledge in this important field of engineering in Iraq. For this purpose, a prototype of CWCT optimized by added packing under a heat exchanger was designed, manufactured and tested for cooling capacity of 9 kW. Experiments are conducted to explore the effects of various operational and conformational parameters on the towers thermal performance. In the test section, spray water temperature and both dry bulb temperature and relative humidity of air measured at intermediate points of the heat exchanger and packing. Exergy of water and air were calculated by applying the exergy

The aim of this paper is to introduce the concept of N  and Nβ -closed sets in terms of neutrosophic topological spaces. Some of its properties are also discussed.

This research deals with the concept of space in the theatrical performance and how the director works between two different spaces, the closed space and the open space. The question was how to use space according to the director's vision in the presentation. The problem of the research was whether the director of the Iraqi filmmaker could see the variable in the architectural space Or the place or space within the exhibition between open and closed, through the formation of the vision of the external components of intellectual and aesthetic and aesthetic, and impact on the relationship between the actor and the recipient to produce a new aesthetic space, and then the purpose of research and importance and limits and terminology The seco