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 importance of research is to be considered by highlighting the tax policy in Iraq which extended for successive measurement of the amount of tax receipts for respective periods, the research problem represents security, economic and political issues that Iraq suffered which were very difficult since Nineties of the last century until now that led to a lake of clarity in tax policy trends, volatility in it and finally reflected on the tax revenues increase or decrease. One of the main recommendations of the research is: (The necessity to develop a deliberate strategy for tax policy in Iraq which should take into account financial, economic, and social goals in appropriate way).

Background: Colorectal cancer is the third most common cancer-related mortality worldwide, and its prevalence is increasing among many nations.  Aim of the study: Investigate the predictive value of carbohydrate antigen 242 (CA242) in comparison to the CEA biomarker and to estimate the significance of CA242 as prognosis maker in colorectal cancer patients. Methods: a case-control study with a total of 150 individuals, 100 patients (59 males, 41 females) and 50 healthy controls (26 males, 24 females). using an enzyme-linked immunosorbent (ELISA) to determine the serum levels of CA242 and CEA. The study was carried out at the gastroenterology consultation clinic of the oncology teaching hospital between November 2020 and February

This study came to discuss the subject of industries dependent on petrochemical industries in Iraq (plastic as a model) during the period 2005–2020, and the study concluded that the plastic industries contribute to areas of advancement and progress and opportunities to deal efficiently with the challenges posed by the new variables, the most important of which is the information revolution. communications and trade liberalization, and this is what contributes to the competitiveness of these industries. And because the petrochemical industry in Iraq has an active role in establishing plastic industrial clusters and clusters of micro, small, and medium industries by providing the necessary feedstock for these industries in various fields

This study aims to isolate the pathogenic yeasts from genital tract and investigate their relationship with the age .The results clarified that the most pathogenic yeast isolated from genital tract was Candida albicans , also the results of C.albicanas isolates susceptibility test, to different antifungal revealed that they were sensitive to Miconazole, Ketoconazole and Clotrimazol and were resistant to Nystatin and Grisofulvin. The study of relationship of vaginal infection with the age showed that the incidence of infection with Candida was high among females age group (19-39 years).