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

        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 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.

The research demonstrates new species of the games by applying separation axioms via  sets, where the relationships between the various species that were specified and the strategy of winning and losing to any one of the players, and their relationship with the concepts of separation axioms via  sets have been studied.

The x-ray fluorescence (XRF) of Znpc molecule with (flow of Ar) and Znpc molecule with (grow in N2) showed two peaks at (8.5and 9.5 Kv) referring to orbital transition ) K?-shell & K?-shell) respectively. The study of x-ray diffraction (XRD) where it was observed good growth of the crystal structure as a needle by the sublimation technique with a ?-phase of (monoclinic structure ) . Using Bragg equation the value of the interdistance of the crystalline plane (d-value) were calculated. We noticed good similarity with like once in the American Standards for Testing Material (ASTM) .Powder Diffraction File (PDF) Program was used to ensure the information obtained from (ASTM) . The output of (PDF) was compared with celn program, where the val

Let R be a commutative ring with non-zero identity element. For two fixed positive integers m and n. A right R-module M is called fully (m,n) -stable relative to ideal A of , if for each n-generated submodule of Mm and R-homomorphism . In this paper we give some characterization theorems and properties of fully (m,n) -stable modules relative to an ideal A of . which generalize the results of fully stable modules relative to an ideal A of R.

This study investigates asset returns within the Iraq Stock Exchange by employing both the Fama-MacBeth regression model and the Fama-French three-factor model. The research involves the estimation of cross-sectional regressions wherein model parameters are subject to temporal variation, and the independent variables function as proxies. The dataset comprises information from the first quarter of 2010 to the first quarter of 2024, encompassing 22 publicly listed companies across six industrial sectors. The study explores methodological advancements through the application of the Single Index Model (SIM) and Kernel Weighted Regression (KWR) in both time series and cross-sectional analyses. The SIM outperformed the K