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 .

Corruption, in all its categories and forms, is regarded as the nowadays virus which has greatly spread in most institutes and society, a matter that cause a great waste of resources.

      According to the reports of international transparency Institute, Iraq is regarded as one of the greatest countries in corruption.

      Regardless of the reasons and forms of corruption, the retreat in work – values and ethics are the main reasons behind that.

      Being the main source of providing qualified staff "educators" for the working market, the high education institutes face great challenges in standing against corruption inside and outside

The makers of strife exist in every era and time. They differ in how these temptations are created and the methods used in doing so. In our modern era, they are more; This is due to the presence of information technology and its easy availability at their fingertips, as well as the spread of social networking sites, which are rapidly spreading among ignorant groups and groups that are deficient in their use. Which led the makers of sedition to exploit these matters and create various temptations and spread them among peoples and societies. Today, we cannot predict the future of humanity in light of this huge amount of temptation. What the Holy Qur’an mentioned about the types of temptations in its noble verses and their embodiment in seve

Objective: The current study aimed to prepare a measure for comprehensive knowledge marketing management. In the Iraqi sports institutions under study, identifying the extent of each dimension of comprehensive knowledge marketing management. Research methodology: This study relied on appropriate scientific methods, mainly represented by the descriptive method and the analytical method, and on the case study method because it suits the nature of the study. The study population was determined from the administrative cadres in the Iraqi Sports Federation, and the research sample numbered (86) and was represented as follows: The preparation sample numbered (50) and a percentage amounted to (58.13%), the sample of the exploratory experim

This paper involved the registration of 1,936 cases of infection of the Leishmania tropica parasite observed at hospitals and health centers in Ramadi, Fallujah, Baghdadi, and Hit during 2017. The results revealed that the highest rates of infection were found in Ramadi and Fallujah. The 1-10 years age group recorded the highest rate at 35.5%. There was no significant difference (p ≥ 0.05) between the sexes. December and January saw the highest rate of infection, where the rate in rural townships was found to be 65.5%, higher than in urban regions which saw a rate of 34.4%. Facial lesions were the most prominent area of infection, recorded at a rate of 41.3%. The study also included an examination of 180 rodents (94 mice and 86 black r

The research aimed to test the effect of independent variables career plateaus and workaholism on employees loyalty through the influence of the mediator variable organizational socialization. Descriptive approach with survey style   on a sample of managers and executives in the Iraqi Drilling Company in Basra's (123) employees. The most important findings of the research are: the existence of a significant effect of the independent variables career plateaus and workaholism in employees loyalty by having a mediator variable organizational socialization and introduced numerical from recommendations.                    &nbs

The recent advances in technology, the increased dependence on electrical energy and the emergence of the fourth industrial revolution (Industry 4.0) were all factors in the increased need for smart, efficient and reliable energy systems. This introduced the concept of the Smart Grid (SG). A SG is a potential replacement for older power grids, capable of adapting and distributing energy based on demand. SG systems are complex. They combine various components and have high requirements for real time reliable operation. This paper attempts to provide an overview of SG systems, by outlining SG architecture and various components. It also introduces communication technologies, integration and network management tools that are involved in SG sys

The financial crises that occurred in South East Asia and America, and the discovery of the financial and administrative corruption that affected these companies, which led to the crisis. Since then, organizations and institutions interested in accounting have begun new ways to further rationalize the management of these companies. Hence the concept of governance, which means good governance. Al-Susiya confirmed its adoption of the financial reporting standards and adopted internal and external auditing for the purpose of increasing the reliability and credibility of the financial and reports that increase the confidence of investors in making their investment decisions in the financial markets The study dealt with the contributi