In this paper we investigated some new properties of π-Armendariz rings and studied the relationships between π-Armendariz rings and central Armendariz rings, nil-Armendariz rings, semicommutative rings, skew Armendariz rings, α-compatible rings and others. We proved that if R is a central Armendariz, then R is π-Armendariz ring. Also we explained how skew Armendariz rings can be ?-Armendariz, for that we proved that if R is a skew Armendariz π-compatible ring, then R is π-Armendariz. Examples are given to illustrate the relations between concepts.

Increasingly important public opinion polls steadily .... especially in electoral campaigns, sheds searchlight on the side of the US elections, in different time periods, and cited the words of experts and people involved in it, and reviews Find great development that took place in the polls and what could happen to this work It is important in the future. Display search for certain types of polls, dividing them on as stated by the experts in the United States... This division shows that the surveys of the most political processes and accuracy of information, and that their Money being made and companies specialized in the administration of this type of measuring public opinion ..... what is returned decision-making, for example, in conj

The presence of research Repositories in the intellectual production of universities and their availability through their websites or through their scientific institutions is one of the criteria for evaluating these universities in the international classifications of the best universities, in addition to preserving the intellectual output of these universities for a long time and safely and preserving the property rights of researchers. And made them available through their websites. The purpose of this research is to identify the concept of digital content and research repositories and its origin, and to indicate the importance of its existence through the websites of universities and their types, and to identify the research repositories

Man has a great role in the development of society in all fields, and therefore the human thought played a great role in its continuous pursuit and insight into the social classes that differ in their privileges, which makes the members of society not reconcile because of that disparity that is not based on human principles, so one class exploits another, and this is what stopped me Rather, it prompted me to choose the topic (class and its impact on society) in order to show the impact of classes on each other negatively and positively, so I work to avoid the first with the recommendations I put forward and offer guidance, and strengthen the second, and after this topic of necessity in a place because of the imbalance and promise of appr

In this paper, we introduce a new concept named St-polyform modules, and show that the class of St-polyform modules is contained properly in the well-known classes; polyform, strongly essentially quasi-Dedekind and ?-nonsingular modules. Various properties of such modules are obtained. Another characterization of St-polyform module is given. An existence of St-polyform submodules in certain class of modules is considered. The relationships of St-polyform with some related concepts are investigated. Furthermore, we introduce other new classes which are; St-semisimple and ?-non St-singular modules, and we verify that the class of St-polyform modules lies between them.

      In this work we discuss the concept of pure-maximal denoted by (Pr-maximal) submodules as a generalization to the type of R- maximal submodule, where a proper submodule  of an R-module  is called Pr- maximal if  ,for any submodule  of W is a pure submodule of W, We offer some properties of a Pr-maximal submodules, and we give Definition of the concept, near-maximal, a proper submodule  

 of an R-module  is named near (N-maximal) whensoever  is pure submodule of  such that  then K=.Al so we offer the concept Pr-module, An R-module W is named Pr-module, if every proper submodule of  is Pr-maximal. A ring  is named Pr-ring if whole proper ideal of  is a Pr-maximal ideal, we offer the concept pure local (Pr-loc

In this thesis, we introduce eight types of topologies on a finite digraphs and state the implication between these topologies. Also we studied some pawlak's concepts and generalization rough set theory, we introduce a new types for approximation rough digraphs depending on supra open digraphs. In addition, we present two various standpoints to define generalized membership relations, and state the implication between it, to classify the digraphs and help for measure exactness and roughness of digraphs. On the other hand, we define several kinds of fuzzy digraphs. We also introduce a topological space, which is induced by reflexive graph and tolerance graphs, such that the graph may be infinite. Furthermore, we offered some properties of th

Jurisprudence purposes Anwash and his importance

Background: Total superficial parotidectomy is the most commonly used approach in excising the tumors that affect the superficial lobe of the parotid gland, whether they're benign or malignant. The aim of the study is to evaluate the benefits and drawbacks of total superficial parotidectomy for parotid gland tumors within five years of follow-up. Patients and methods: Nineteen patients with lateral facial swelling affecting the parotid region were included in this study. All of them operated under general anesthesia with oral endotracheal intubation, where Modified Blair Incision (lazy S incision) was utilized in all cases. Anterograde dissection with facial nerve identification was accomplished with total superficial parotidectomy.