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 .

Singing has significant importance being a major basis for the expressive and cultural production of the societies and a real companion that reflects their artistic career and is strongly connected to the reality of the peoples and the production of the individuals, who are geniuses of arts and culture.
Rural singing represents one of the most well-known artistic singing styles in Iraq, which truly embodied the Iraqi national identity. However, it remained confined to the countryside and did not spread due to the lack of mass media and the recording technologies at that time. It has been pure virgin singing art. The theoretical framework is divided into three axes:

• The Iraqi singing heritage in the twentieth century, a hi

The phenomenon of negative behavior has studied as a social and psychological phenomenon that effect on the performance and life of workers inside and outside the organization. The adoption of this phenomenon is studied in terms of the role of the internal environment of the organization in addressing this behavior, being the variables belong to the field of organizational behavior to see the results of those variables on the Iraqi organizations, since the specificities of it differ from the rest of the Arab and foreign environments. Therefore, this study focused on testing the relationship of the internal environment of the organization and its role in addressing the negative behavior of the workers.

thi

Since the nineties of the last century, Iraqi youth have been exposed to Mexican soap operas dubbed into classical Arabic, and the stories and ideas presented by these series were almost new to all the minds of the youth at that time, a culture completely different from the culture we have of social relations, and since the number of episodes was more than Of the 100 episodes, exposure to these series has left young people confused by the addiction to all their ideas and stories. They differ from the foreign films (mostly American) that we used to watch, and they only take two hours (at most). These films contain diverse stories and may be forgotten. Memory includes events and characters in their entirety at times, and you may remember th

A case-control study was designed to find out the association between rs2234671 polymorphism of cxcr1 and rUTI in a sample of Iraqi women by polymerase chain reaction- sequence-specific primer (PCR-SSP) method. The current findings revealed that the genotype GC (OR= 7.86, 95% CI = 2.82-21.87, P= 7.7 × 10-5) and the C allele (OR= 3.93, 95% CI = 1.97 - 7.83, P = 9.8×10-5) are significantly associated with rUTI. However, the genotype GG played as a protective factor (OR= 0.12, 95% CI = 10.05 - 0.34, P = 4.0 ×10-5). Depending on these findings, the genotype GC is significantly associated with rUTI.

This study dealt with the presentation and documentation of the Iraqi women's participations in athletics in the Arab sports courses since the establishment of the Federation of Athletics in 1948 to 2017 as well as analysis of the results achieved for these participations and discuss the reasons for not participating in some of these courses and the researchers try to show the distinct role of Iraqi athletes, And their active contribution to these courses to represent the country as well as to promote the sports reality of Iraqi women compared to their Arab sisters, whose names have become a symbol of every Arab woman and therefore benefit from the experience of the Arab teams In athletics for women.

This paper discusses the role of Auditors' Technological Maturity in reinforcing the quality of auditing profession, through focusing on the concepts of Technological Maturity and quality of auditing profession, as well as designing a proposed model for Technological Maturity which includes five evolutionary and sequential stages, and this proposed model would contribute to reinforce the quality of auditing. This proposed model will be employed in the field of auditing profession because the importance of the development and investment in this profession and the importance of the need for specialized knowledge in Information Technology, and the result of a proposed model is development of technological knowledge for the auditor to reach

This research began by explaining its variables and dimensions especially the digital gap, which the authors explained it elaborately beginning with the concept, the reasons blind its emergence of its measurement, and how to treat it. The authors supposed the potentiality of relying on enforcing knowledge in general and the groups suffer from this gap in particular, especially the targeted knowledge to treat its subject.

As enforcing knowledge usually depends on some strategies or choices of organizational orientation among them is learning and training from one side, and communication, as an indicating factor for organizational effectiveness as the authors refer from the other side.

The current research aims to test the effect of knowledge sharing in its dimensions represented by(individual dimension, organizational dimension, and technological dimension), In reducing the strategic Anxiety of Iraqi Airways, In view of the importance of the two variables for the company from the perspective of society and the sample resulting from directing various organizational phenomena to reduce its strategic Anxiety, As a goal, it should be viewed from multifaceted perspectives(uncertainty, relational disorder, competitive disorder, resource depletion), And it was embodied by choosing the descriptive, exploratory approach, as it is the most appropriate in that aspect, so that the research questionnaire is one of solid scientific