In this paper, we develop the work of Ghawi on close dual Rickart modules and discuss y-closed dual Rickart modules with some properties. Then, we prove that, if are y-closed simple -modues and if -y-closed is a dual Rickart module, then either Hom ( ) =0 or . Also, we study the direct sum of y-closed dual Rickart modules.

The scholars of Iraq in the modern and contemporary era have been interested in the definition of tremendous knowledge treasures left by the successive Iraqi civilizations on Mesopotamia and around the cities, through the census and extrapolation of manuscript heritage and even printed, they compiled indexes,evidence

     Islamic manuscripts are considered an identity for the civilizational, cognitive and cultural development of nations and the Islamic world as a whole, and to identify this identity

The increasing rates of consumption of cigarettes harmful, to health in the world in general, and in Iraq in particular, and because of the costs borne by individuals, and the state as a result of addressing its damage, as well as Iraq's commitment, to international conventions against cigarettes, and demands of the World Health Organization, to raise prices to reduce consumption. Therefore, the tax Selectivity is one of the most important ways of regulating the consumption of this commodity on the one hand and increasing the tax revenue on the other. The research aims to shed light on the issue of selective tax on cigarettes and the impact of their application in increasing tax revenues and identify the effectiveness of the application

     Islamic manuscripts are considered an identity for the civilizational, cognitive and cultural development of nations and the Islamic world as a whole, and to identify this identity, the closing statement usually written at the end of the manuscript helps us with this, meaning that the closing entries serve as the identity document of the manuscript

استخلص عامل التلزن من E. faecalis EM1 بعد تكسير الخلايا بعدة طرق واختيار الطريقة التي تعطي اعلى قيمة تلزن والترسيب بالكحول الاثيلي , واجري فحص التلزن وقياسه للمستخلص  مع انواع من البكتريا السالبة لملون غرام تضمنت     Escherichia coli  و Klebsiella  pneumoniae  و Serratia

The strong cryptography employed by PGP (Pretty Good Privacy) is one of the best available today. The PGP protocol is a hybrid cryptosystem that combines some of the best features of both conventional and public-key cryptography. This paper aim to improve PGP protocol by combined between the Random Genetic algorithm, NTRU (N-th degree Truncated polynomial Ring Unit) algorithm with PGP protocol stages in order to increase PGP protocol speed, security, and make it more difficult in front of the counterfeiter. This can be achieved by use the Genetic algorithm that only generates the keys according to the Random Genetic equations. The final keys that obtained from Genetic algorithm were observed to be purely random (according to the randomne

A new human-based heuristic optimization method, named the Snooker-Based Optimization Algorithm (SBOA), is introduced in this study. The inspiration for this method is drawn from the traits of sales elites—those qualities every salesperson aspires to possess. Typically, salespersons strive to enhance their skills through autonomous learning or by seeking guidance from others. Furthermore, they engage in regular communication with customers to gain approval for their products or services. Building upon this concept, SBOA aims to find the optimal solution within a given search space, traversing all positions to obtain all possible values. To assesses the feasibility and effectiveness of SBOA in comparison to other algorithms, we conducte

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