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 .

The existence of succession system has appeared in Arab Islamic state after the death of the prophet Mohammed (peace be upon God and peace), So there was caliphate, then the Umayyad dynasty in Syria , until 132 AH , the date o the emergence of the Abbasid state adopted a system ministry formally , hafs bin sulaiman ( Abu salamah Khallal ) was the first  minister emerged on the political scene. He was killed at the time of the first  Abbasid caliph , Abu Albbas , incest 132-136 who had put Khalid bin barmak as a minister instead of Hafs bin Sulaiman . During the reign of AL-Mansur 136-158 , there was an importance and a place for the ministry , despite of AL-Mansur strength personality that covered on his ministers personalities

shoulder joint by preparing special exercises for the youth-category wrestling, and through the researchers' follow-up to the wrestling game and their work in the field of rehabilitation and physical therapy, noticing that most of the wrestling players suffer from the shoulder joint pain despite their visit to the specialist doctor and take Treatment, so the researchers saw to study this problem and restore the recovery of the injured through special exercises and a suitable qualification program for the shoulder joint muscles, the goal of research in preparing special exercises and knowing its effect on the rehabilitation of the background muscle of the shoulder for the youth wrestling category. The researchers assumed that there are stati

   يهدف البحث إلى التعرف على The research aims to identify the effect ofاثر التركيب العمري للسكان على الناتج المحلي الإجمالي في العراق وتحديد الفئات العمرية من أطفال ومنتجين أي من هم في سن العمل والمسنين لأهمية ذلك لإغراض التخطيط الاقتصادي.إنeffectofeee age structure of the population on GDP in Iraq and determine the age groups of children and any of the producers wham are of working age and the elderly of the importance for the purposes of economic planning. نسبة الفئة العمرية Proportion of the age group (00- -4 4سنوات اقتربت من

This research aims to identify the factors effecting the investigation of insurance fraud from the perspective of the National Insurance Company employees, by analyzing the study variables and make recommendations on how to enhance the company and employees performance, and to achieve the objectives of the study and test hypotheses a questionnaire was designed after referring to the international standards  and the 1969 Iraqi punishment law, and it was answered by 20 employees that were approved for the purposes of  this research and analysis.

      The study found that lack of employee training was a strong factor, while the supervisory staff and operational procedures was a weak one.

G

             A discussion about the repercussions of the exchange rate on the behavior of stock markets became one of the basic principles of financial economics. The Istanbul Stock Exchange , considered  one of the fastest financial markets growing in the region, driven by solid economic activity, for a diversified economy  which classified as one of the the fastest growing economies in the world. However, the aforementioned market witnessed sharp fluctuations in the past few months, coinciding with the continuous fluctuations in the exchange rate of the Turkish lira, posing a serious challenge to the economic and investment environment in a c

The research dealt with the effect of Kut Barrage on the geomorphological processes and the natural environment system in the course of the Tigris between the cities of Al-Ahrar and Kut in central Iraq. It was clear from the research the contribution of Kut Barrage in changing the surface runoff system between the front and back of the barrage, as well as changing the type of processes and the prevailing geomorphic forms, as the sedimentation activates the front of the barrage and erosion at its back, which affected the change in the morphology of the river, sediment retention at the front of the barrage, the burial of the bottom and reducing the validity of the stream. This also affects the efficiency of the barrage’s work and coastal er

The current research aims to assess the Brief Book of the Modern and Contemporary History of Asia from the perspective of the students in the Department of History, University of Baghdad. The study is carried out in Iraq and the research group has included students of the Department of History in the College of Education--Ibn Rushd and the College of Education for Women- University of Baghdad. The chosen sample of the assigned research consisted of (72) students from third stage in the Department of History, which equals (0.38%) of the total group members amounted (188) female and male students representing (40) students from the College of Education--Ibn Rushd, and 32 students from

Current research targeted: Recognizing the impact of the differentiated education strategy on the achievement of the students of the Institute of Fine Arts / Diyala, for the academic year (2018-2019).
The researcher used the experimental approach designed by two groups (control - experimental) and with a post-test to achieve the goal of the research, and the research sample was chosen from students of the fourth stage for the academic year (2018-2019).
The sample was distributed randomly into two groups, the first experimental consisting of (30) students who studied using the differentiated education strategy, and the second control group consisting of (30) students who studied using the traditional method.
The researcher pre

Background: Peripheral giant cell lesion (PGCL) and central giant cell lesion (CGCL) of the jaws have a distinct clinical behavior.Giant cell tumour (GCT) is a benign locally aggressive neoplasm affects the long bones. Both lesions are characterized histologically by multinucleated giant cells in a background of ovoid to spindle-shaped mesenchymal cells. The WW domain-containing oxidoreductase (WWOX) gene is located at 16q23.1–16q23.2, a region that spans the second most common human fragile site, FRA16D, at 16q23.2.The Ki-67 antigen is a nuclear protein that is associated with and may be necessary for cellular proliferation.Ki-67 protein is present during all active phases of the cell cycle (G1, S, G2, and mitosis), but is absent fr