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 .

Abstract
        This research aims to identify the relationship and the impact of the behavior of organizational citizenship in the performance of employees, as practiced behaviors organizational citizenship substantial role in achieving the objectives of both the organization and its staff at the same time, so it affects a large extent on the characteristics and performance of individuals employees and thus influence the success of the organization as a whole, problem of the research has indicated that there is a clear failure in the study of the impact of the behavior of organizational citizenship in the performance of employees, was chosen

The research aims to identify the impact of the merger of the companies affiliated to the Ministry of Industry and Minerals on their financial profitability since the companies before the merger suffered a rise in losses and the deficit reached very high levels that affected its overall performance and even on the morale of workers as losses are increasing and solutions Efficiency is absent. The problem stems from knowing the impact of the merger on the profitability ratios of the companies. The research field was represented by the companies affiliated to the Ministry of Industry and Minerals (21) companies, while the research sample reached (6) companies after the merger (14) companies before the merger, was based on data The f

The study aims to find out the effectiveness of using the Google classroom educational platform in teaching mathematics curricula from the viewpoint of teachers in the Governorate of Al Dhahirah, Sultanate of Oman. The researcher adopted the descriptive-analytical approach. To collect the needed data, a questionnaire of two dimensions was used. It includes (13) items to measure the effectiveness of using the Google classroom in teaching mathematics curricula from the teacher's point of view and includes (10) items to measure the difficulties of using the Google classroom in teaching mathematics curricula from the teachers' point of view. These tools were applied to (32) male and (31) female as the study sample. They represent mathematics

This study included an analysis of three stations (Al Dora, Al Za'franiya, and Arab Ejbur) chosen to study the Physiochemical and microorganism (Fungi and Bacteria) loud of the Tigris River in the southern section of Baghdad city. The result of this research shows that the highest temperature recorded in summer in Al Za'franiya was 37Co, while the lowest temperature recorded in winter in Al Dora was 9Co. and the value of pH recorded the highest in summer it was 7.9 in Arab Ejbur, and the lowest value was in winter 7.1 in Al Dora regions, While Total Organic Carbon (TOC) shows the highest values found in the summer was 6.7 Mg L-1in Al Za'franiya Samples, and the lowest values were 2.0 Mg L-1in Arab Ejbur during the winter. The more f

The  adopted method in the teaching of history is conservation and indoctrination in all grades, and this will lead to a lack of students interact with teachers in the course of the lesson, and poor use of teachers to questions that raise students' thinking during the lesson, which leads to a lack of interest in the topic of the lesson and wasting opportunities contribution making it the teacher at the center of the educational process, and to provide arrogating the researcher to contribute to teaching style with the belief that the use of this method of teaching could lead to overcome the difficulties and problems faced by the teaching material.

And there are educational complexes integrated approac

The aim of the research is to identify the imaginative thinking skills included in the content of the chemistry textbook for fifth-grade students in biological sciences at the preparatory stage, which is approved by the Ministry of Education, General Directorate of Curricula in the academic year 2020-2021. To achieve the objective of the study, the researcher depends on the previous studies in the field and content of imaginative thinking skills for preparing a list of skills that includes (3) essential skills and (11) sub-skills and (28) items related to all skills. The researcher adopted the analytical descriptive approach because of its appropriation of the goals of the research. Then the researcher analyzed the content of the book de

The sustainable competitive advantage for organizations is one of the requirements for value creation, which centered on the possession of scarce resources that achieve maximum flows to invest in intellectual capital, if what has been interest in them, measured and employed the way properly and style, so I figured the need for new technologies to enable organizations to measure the intellectual and physical assets and to assess its performance accordingly, so it sheds search light on the measurement of the added value of existing knowledge using the standard value-added factor is the intellectual (value added intellectual coefficient) (VAIC) and to develop a set of assumptions about the extent of the difference between the sample

This study aims to the little impact of accounting financial performance (AFP) analysis on the money market in the Iraqi economy. Potentially limiting future market activity could be international risks and obstacles, which in turn could cause issues and crises (Shah & Jan, 2014; Bakhtiyarovich, 2020)‏. The study concept was inspired by the recognition that there must be communication between the importance of the AFP analysis of the Iraqi securities market and the country’s financial and economic institutions. The sample of the study included ten Iraqi banks listed in the Iraq Stock Exchange (ISE) for the period 2010–2020. The three mathematical models included in the statistical analysis served as the basis for projectin

Abstract

The aim of the research is to introduce the international standards of the Supreme audit Institutions, as well as the role of these standards in achieving administrative reform and improving the performance of the Supreme audit Institutions and the performance of the economic units under its control.

In order to achieve the objectives of the research, a questionnaire was designed from two main axes that included a number of questions addressed to a number of officials and employees of the Supreme Audit Institutions and its affiliated bodies on the role of applying the international standards of the Supreme Audit Institutions in achieving administrative re