In this paper we generalize Jacobsons results by proving that any integer  in   is a square-free integer), belong to . All units of  are generated by the fundamental unit  having the forms

Our generalization build on using the conditions

This leads us to classify the real quadratic fields  into the sets  Jacobsons results shows that  and Sliwa confirm that  and  are the only real quadratic fields in .

    رافقت القسوة الانسان منذ القدم  وكثيرا ما تم الخلط بينها وبين العنف لشدة التقارب بينهما , وهنا يحاول البحث  ان يفصل بين كلا المفهومين ويتفرد بمفهوم القسوة, الذي سلط عليه الضوء في المسرح لأول مرة على يد الفرنسي(انطوان ارتو)  في محاولة للكشف عن المعالجة الاخراجية التي قدمها المخرج العراقي(صميم حسب الله) لمفهوم القسوة في مسرحيته الموسومة (خريف) ويتضمن البحث نبذه  (مفهوم القسوة في الفكر الانساني) وكذلك (الق

Arts acts to reduce and exclude everything that is not necessary in the delivery of meaning, especially representative performance, which is based on the intensification of the physical and vocal actions, and in drawing the dimensions of the character. And because that, the artistic staff, among others in the ministry of education, are considered the cornerstone, in the development of theatrical activities in schools, this research came to find out the extent to which teachers in primary schools, in secondary schools and artistic supervisors rely on shorthand mechanisms in the representative performance.
The current research relied on the descriptive approach, in analyzing his sample, which was deliberately chosen, Among the most imp

The literature shows conflicting outcomes, making it difficult to determine how e-learning affects the performance of students in higher education. The effect of e-learning was studied and data has been gathered with the utilization of a variety of qualitative and quantitative methods, especially in relation to students' academic achievements and perceptions in higher education, according to literature review that has been drawn from articles published in the past two decades (2000-2020). The development of a sense of community in the on-line environment has been identified to be one of the main difficulties in e-learning education across this whole review. In order to create an efficient online learning community, it could be claim

the research was exposed to a study the importance of the role of the supportive entities in providing the useful information to the tax administration and their ability to extend the level of the tax base of taxpayers, through the improvement of the tax payers determination and their tax settle for the purpose of increasing the tax revenue, and shed light on the legal evidence through which these entities become officially assigned to perform a supplementary task to the General Committee for Taxes GCT, to help it to perform its task efficiently, and to study the reasons of the weak cooperation of the supportive entities and their reluctance to provide useful information which leads to limiting the tax base.

The research data hav

Background. Teaching quality in gymnastics is influenced by teachers' performance and attitudes, leading to increased functional creativity and psychological well-being. This, in turn, contributes to the success of the sports institution by enhancing the overall performance and overall well-being of the students. Objectives. The research aims to assess the psychological well-being and functional creativity of female gymnastics professors in Iraqi colleges of physical education and sports sciences, focusing on their level of well-being and the relationship between these factors. Methods. The researchers used a descriptive survey method to survey female gymnastics professors at 16 colleges in Iraq's physical education and sports science

This research set to indicate the role of the opportunity cost in the overall economic development (human and social development) by selecting the most appropriate alternative for the growth of the country in exchange for sacrificing profit limits to achieve this growth and development of the country, especially in the present circumstances of the country and after studying the reality of the economic case for him, as the problem lies with don't selecting the best alternative that enhances the gross domestic product, which extends to promote overall economic development and revive the industrial and agricultural sectors, productivity is more like Impotent, versus sacrifice alternative consumption may bring more financially lucrative than

The research aims to identify the obstacles facing the application of electronic management in our university libraries, including the central library of the University of Baghdad and the central library of Al-Mustansiriya University, the research sample, as they are among the main libraries that used electronic technologies in managing some of their work and in providing their services, and they have a website via the Internet. The research relied on the case study method to identify the obstacles by visiting the two libraries, interviewing their managers and employees responsible for the departments, and answering inquiries about the obstacles that prevent the application of electronic management in order to identify them and find appropr

Abstract

The pressures of life have become a tangible phenomenon in all societies in varying degrees. This disparity determines several factors, including the nature of societies, the level of their urbanization, the intensity of interaction, the intensity of conflict, and the increasing rate of change in those societies. many people name The modern era in which we live the “era of pressures", where one of the most important of these changes is the “new Coronavirus 19-COVID”, which has spread widely throughout the world, as the pandemic, has affected all aspects of daily life, including the educational and academic process, academic activities have been suspended in universities, which caused sudden change

The research aimed to prepare a measure of job stressors affecting the quality of teaching performance in the College of Physical Education and Sports Sciences at the University of Baghdad, to identify their levels, if any, and the most influential dimensions on the quality of teaching performance within the college’s work environment, as well as the deanship’s ability to help prevent and Alleviating its severity through logical administrative methods, on a scale that includes four dimensions that include (the administrative and financial environment, the organizational environment, the social and humanitarian environment, and the scientific and research environment). The descriptive approach was adopted using the case study met