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 objective of this study is to attempt to provide a quantitative analysis to the causes of unemployment  in Iraq and its mechanisms of generation, as well as a review of the most important  types of both visible and invisible unemployment, and an attempt to measure the disguised  unemployment  and analyze the causes. The problem of the research lies in the fact that the Iraqi Economy has been suffered  for  a long time although its characterized by abundant  physical and natural  resources, from the existence of the  phenomenon of unemployment  in the previous two types. Causing a lot of economic problems, represented by the great waste of resources and

Provides the style of benchmarking the best possible use whenevaluating the performance and evaluation, as well as improved performance,due to its consistency with the principles of good evaluation of theperformance, an extension of the completion of several functions of the timeand cost less, thereby increasing the efficiency of the management of theinstitutions, especially institutions, the media, as it became public the future ofthe message sender to the same time Zaorosaúl new media is challenging thetraditional media of what distinguishes this new interactive media and mass ledto this transition . However, the media Aljdidhoosaúl traditional mediacontinue to coexist and reinforce each Menhmaalakhr, for his wealth offreedom of opin

The goal of the research is to identify the effectiveness of using a proposed strategy according to the Fraunhofer model of knowledge management in mathematics achievement for second-grade female students in middle and high schools affiliated with the General Directorate of Education in Baghdad / Al-Karkh II. The objective was to prove the following null hypothesis: "The average scores of the experimental group who will study with the proposed strategy according to the Fraunhofer model and the scores of the control group students who will study in the usual way in the mathematics achievement test are not statistically significant different at the significance level (0.05)." The General Directorate of Education of Baghdad / Al-Karkh

t. The current study was conducted on the umbilical cord blood of newborns in the Banks Hospital in Baghdad, Diyala, and Khalis in Diyala, where the study included 90 samples of blood, and samples were collected for the period from the 1st of October;2020 to The first of February;2021 AD, where the study included measuring levels of interleukin-6;Adiponectin,glucose and bilirubin in the blood, comparison study between the study variables with the child's weight (greater than 3 kg),(less or equal 3 kg),the mother's age (greater than 25 years, less or equal to 25 years),the sex of the child (male, female).The results of our study showed that there were no significant differences between the variables of the current study between the two sex

Abstract

This research aims to determine the role of the quality of higher education in achieving organizational excellence at the universities of Baghdad and Al-Nahren, was based on research on the main hypothesis is:First:- There is correlation and between the quality of higher education dimensions (continuous improvement, measurement and analysis, the culture of the organization, optimal use of resources , customer satisfaction) and organizational excellence dimensions (strategic planning, focusing on the market and the customer, information and analysis, the effectiveness of operations, processes and resources), Second:- Second, there is the impact of relationship sig