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 study aimed to investigate the effect of fungicides chlorothalonil at different concentrations ( 0.1 , 0.5 , 5 , 25 , 50 ) × 10 - 5 M on some cytogenetic parameters of human peripheral blood lymphocytes . The genotoxicity parameters were estimated by the number of chromosomal aberrations (CAs) and their types and by estimating the induced micronuclei (Mn) . Cytotoxic effect recorded by estimating the mitotic index (MI) . Results revealed that the fungicide increased the CAs in dose – response pattern with positive correlation coefficient ( r = + 0.964) , there was a significant differences among the concentrations (P<0.01) . The major CAs records chromosomal breakage at concentrations. 0.5 , 5 , 25 , and 50 , while the lowest concen

The present study is concerned with studying the effect of aquatic plant Hydrella vorticellata with the concentration of 10 and 20 gm/2 K gm soil on percentage and growth rate of germinating seeds of Hordeum vulgare and Vicia faba. More overs, the quantitative amount of NPK in both tested plants and Hydrella vorticellata, are estimated as an organic fertilizer. It has also been find the total number of root cells, the number of dividing cells, and stages of mitosis. The study reveales, that there are no significant differences between the concentration of hydrella used in germination percentage, growth rate, wet and dry weight. While there are differences in the plants containing NPK. The number of cells dividing stages and number of divid

This study was conducted in the poultry fields of the College of Agricultural Engineering Sciences / University of Baghdad from 10/15/2021 to 11/25/2021.To know the effect of adding different levels of Ganoderma lucidum to broiler diets on productive performance. 200 unsexed (Ross 308) chicks of one day age with a starting weight of (40) g were used. The chicks were randomly distributed into four treatments and 50 birds. One treatment included five replicates (10 birds/replicate), and the experimental treatments was as follows: T1, T2, T3, T4, and the percentages of adding reishi mushroom were 0, 0.5, 1, and 1.5 g/kg of feed, respectively, and the birds were fed on three starter diets, growth and final diets, The results of this stu

study aims to examine education and the challenges of globalization in light of Corona pandemic. The examination involves surveying a randomly selected sample from the University of Baghdad’s professors, particularly from the colleges of Education for Women, Arts, and Sciences. The purpose of this examination is to learn about the dimensions of globalization, its effects on the educational process, and the importance of distance education during the spread of Corona virus quarantine. To achieve this, the researcher followed a descriptive and analytical approach by applying a questionnaire to a sample of 70 teachers who were randomly selected electronically. Results have shown that 78.6% emphasized the contribution of globalization duri

The study aims to indicate the role of the mechanisms and principles of corporate governance in the activation of social responsibility reports, and increase disclosure, to achieve sustainability, legitimacy, and integrity of the business. Through the presentation of the conceptual framework for corporate governance and social responsibility, identify the key dimensions of social responsibility and the statement of the relationship between the mechanisms of governance and social responsibility reports in accordance with these dimensions. To prove the hypothesis research has selected a sample of listed companies in the Iraqi market for securities,

   الضاد والظاء موطن تفرد العربية وفخرها ، الفت فيهما العشرات والعشرات من المصنفات الثرّة لكثرة ذرائع تلابسهما والخلط بينهما ، فهما متشابهان في هيكل البناء ، وإخراجهما متداخل على اللسان ، وألفاظهما متناظرة برحابة في الإملاء ، فضلاعن  اشكالهما  إلى حدّ الآن ، مما حثني على التفكير في وسائل تسهل المطروح وتمد جسراً بين أجزائه عسى أن تدنو قطافه في دفع الشبهة ومواراتها ، فتحصلت لي امور ادرتها بكلمتين مف

Background: The oral cavity is considered as a complex ecological niche, its complex microbial community is reflected to it. Streptococcus mutans has been implicated as one of the major etiological factor of dental caries. Tooth surfaces colonized with Streptococcus mutans are at a higher risk for developing caries, while lactobacilli are considered as the secondary invaders, not initiators of the carious lesion. The main purpose of this study was to correlate the dental caries (for primary and permanent teeth) in the upper jaw with the streptococcus mutans and lactobacilli count in the dental plaque and saliva, also to correlate the dental caries (for primary and permanent teeth) in the lower jaw with the streptococcus mutans and lactobaci