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 .

This study was done at Al-Balad City Hospital on 60 diabetic patients (25 male and 35 female). The study included Fasting Blood Sugar and fungal diagnosis (systemic and superficial fungus). The results showed that the high concentration of blood sugar belonged to the group > 70 years among the diabetic patients with high significant differences in comparison with other groups P<0.001 . The result showed that percentage of female systemic fungus infection was higher than male systemic fungus infection ( female 63% and male 24%) and vice versa about superficial fungus infection (female 37% and male 76%) . Data showed that the percentage of nail fungus infection among female diabetic patients was higher than the percentage of male diabetic p

      The Green Productivity topic is considered as one of  the more conceptual novelty in the field of Production and Operations Management, and one of the least topics addressed in the literature competent, Green Productivity (GP) is a strategy for enhancing a business's Productivity and environmental performance at the same time, for overall socio - economic development, It is  the application of appropriate techniques , technologies , and management systems to produce environmentally compatible goods and services. the research aimed to find the contribution of this concept for success the industrial Organizations.

The education sector suffers from many problems, including the scarcity of schools that can absorb the increasing number of students in light of the increasing population growth rate, as some regions suffer from a lack of opening of new schools or the expansion of existing schools to increase their capacity so that attention is required. The research sought to identify the level of maturity of project management at the research site (Building Department in Al-Karkh I/ Ministry of Education) Being responsible for educational projects and their implementation and to know that, the ten areas of the knowledge guide to project management PMBOK have been adopted according to the PM3 model (one of the models of maturity

       The study aimed to determine the extent of market knowledge in the companies researched, as if market knowledge is qualified to lead the companies researched to achieve marketing performance , for this purpose, formulated hypotheses of the study in three hypotheses, the first major hypothesis "there is a correlation with significance of market knowledge to improve the marketing performance  , "while the second major hypothesis, "there is a significant moral influence of market knowledge to improve the marketing performance  " these hypotheses targeting to determine the role played by market knowledge in the leadership of companies researched to achieve improvement in marketing perfor

The marketing of banking service is considered to be one of the impotent fields which showed a universal inebriates . He research showed the comparison between the application of marketing in ideas and application for loot government and private Iraqi bank. The research comets of four parts; Mythology / the concept and the importance of Banking Marketing / Research applichlion/ Conelnion and  recommendation.

 The aim of this study was to provide an overall assessment to the efficiency of the Iraq stocks exchanges (ISE) through specifying well –known models .First, Fama's efficient market hypothesis as a contrary concept to the random walk hypothesis, was performed and it has been found that ISE follows the random process, so the price of the shares can't be predicated on the basis of past information. Second,we use a multifactor model, which so named multiple regression, to explore the link between ISE  and the main economic indicators. our empirical analysis finds that every weak associations exists between major ISE measures and main economic indicators.

Determining risk indicators for dental implants is an essential strategy for preventing peri-implant diseases and effective diagnosis of dental implant success. To investigate the impact of certain potential factors on the osseointegrated dental implant. Eighty-four individuals were included in our study, 50 cases as a patient’s group and 34 participants as a control group. All cases were diagnosed based on certain criteria, 30 (60%) of patients had peri-implantitis, 20 (40%) with severe periimplantitis, 36(72%) were generalized, and 15 (30%) as localized peri-implantitis cases. The study has indicated that 44.7% of dental implants were in the anterior maxilla, followed by (27.3%) posterior maxilla, (17.4%) posterior mandible, and (10.4%)

    In the drilling and production operations, the effectiveness of cementing jobs is crucial for efficient progress. The compressive strength of oil well cement is a key characteristic that reflects its ability to withstand forceful conditions over time. This study evaluates and improves the compressive strength and thickening time of Iraqi oil well cement class G from Babylon cement factory using two types of additives (Nano Alumina and Synthetic Fiber) to comply with the American Petroleum Institute (API) specifications. The additives were used in different proportions, and a set of samples was prepared under different conditions. Compressive strength and thickening time measurements were taken under different conditions. The amoun