This dissertation depends on study of the topological structure in graph theory as well as introduce some concerning concepts, and generalization them into new topological spaces constructed using elements of graph. Thus, it is required presenting some theorems, propositions, and corollaries that are available in resources and proof which are not available. Moreover, studying some relationships between many concepts and examining their equivalence property like locally connectedness, convexity, intervals, and compactness. In addition, introducing the concepts of weaker separation axioms in α-topological spaces than the standard once like, α-feebly Hausdorff, α-feebly regular, and α-feebly normal and studying their properties. Furthermor

Suppose R has been an identity-preserving commutative ring, and suppose V has been a legitimate submodule of R-module W. A submodule V has been J-Prime Occasionally as well as occasionally based on what’s needed, it has been acceptable: x ∈ V + J(W) according to some of that r ∈ R, x ∈ W and J(W) an interpretation of the Jacobson radical of W, which x ∈ V or r ∈ [V: W] = {s ∈ R; sW ⊆ V}. To that end, we investigate the notion of J-Prime submodules and characterize some of the attributes of has been classification of submodules.

We define and study new ideas of fibrewise topological space namely fibrewise multi-topological space . We also submit the relevance of fibrewise closed and open topological space . Also fibrewise multi-locally sliceable and fibrewise multi-locally section able multi-topological space . Furthermore, we propose and prove a number of statements about these ideas. On the other hand, extend separation axioms of ordinary topology into fibrewise setting. The separation axioms are said to be fibrewise multi-T0. spaces, fibrewise multi-T1spaces, fibrewise multi-R0 spaces, fibrewise multi-Hausdorff spaces, fibrewise multi-functionally Hausdorff spaces, fibrewise multi-regular spaces, fibrewise multi-completely regular spaces, fibrewise multi-normal

In this research note approximately prime submodules is defined as a new generalization of prime submodules of unitary modules over a commutative ring with identity. A proper submodule  of an -module  is called an approximaitly prime submodule of  (for short app-prime submodule), if when ever , where , , implies that either  or . So, an ideal  of a ring  is called app-prime ideal of  if   is an app-prime submodule of -module . Several basic properties, characterizations and examples of approximaitly prime submodules were given. Furthermore, the definition of approximaitly prime radical of submodules of modules were introduced, and some of it is properties were established.

Let  be a commutative ring with identity, and  be a unitary left -module. In this paper we introduce the concept pseudo weakly closed submodule as a generalization of -closed submodules, where a submodule  of an -module  is called a pseudo weakly closed submodule, if for all , there exists a -closed submodule  of  with  is a submodule of  such that . Several basic properties, examples and results of pseudo weakly closed submodules are given. Furthermore the behavior of pseudo weakly closed submodules in class of multiplication modules are studied. On the other hand modules with chain conditions on pseudo weakly closed submodules are established. Also, the relationships of  pseudo weakly closed

The research issue and its importance concentrate on the importance of choosing and
preparing the kindergarten's teacher educationally ,psychologically and artistically ,and other
aspects because of their need for several skills such as the drawing skill for kindergarten
curriculums include a various artistic experiences and activities as well as for the drawing
importance for the child .And from this, the research goals raise from to prepare a test that
measures the drawing skill for kindergarten students and measure the drawing skill in all four
kindergarten students at the kindergarten department and recognize the differences level for
these students . In order to achieve the first goal in the research ,the resear

The research aims to examine the effect of KUD strategy on acquiring the grammatical concepts among intermediate school students. To achieve the research objective, the researcher adopted the null hypothesis in which there is no statistically significant difference at the level (0.05) between the average scores of students of the experimental group who study grammar base on the KUD strategy and the average scores of the control group who study the grammar through the traditional way of acquiring grammatical concepts. In a random manner, the researcher selected the research sample from one of Baghdad’s education schools in al Rusafa / 2, as the total number of students of the two groups reached (67) students. They were divided into (33)

This research deals with the risks of non-compliance and its impact on the profitability of Islamic banks. Research variables were measured and analyzed as the risk of non-compliance as an independent variableand profitability as a dependent variable. The profitability was measured by three indicators ((rate of return on assets, rate of return on equity and rate of return on Total deposits)) The results of the research showed a significant relationship between the risk of non-compliance and the rate of return on assets and rate of return on total deposits, while there was no relationship between the risk of non-compliance and rate of return on ownership. The research recommended that the senior management of the Islamic Investment Bank s