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 the study stems from the fact that Iraq’s economy is facing a housing crisis, especially in the Iraqi capital, Baghdad, great demographic pressure due to pronounced population growth over the past two decades. The Central Bank of Iraq undertakes several initiatives represented in granting real estate loans, mainly through the Real Estate Bank at very low interest, and in the last two years, the interest has become zero. The purpose of the study is to analyze the fiscal implications of the Iraqi central bank’s real estate initiatives, as well as its real impact on the spatial dimension of the Iraqi governorates through new housing in those governorates. Using data mainly from the Central Bank of Iraq’s bulleti

Many people take protein supplements in an effort to gain muscle. However, there is some controversy as to whether this is really effective. There is evidence suggesting that consuming high level s of protein may in fact have negative side effects for health. The current study included 29 young Iraqi building muscles in two different groups (taken and not protein supplements) (age range=17-31 years), the cases were selected from family, friends, college students, and Gyms), from November 2014 to March 2015. A careful history was obtained from each volunteer including age, duration of sports, type of supplements, and family history of diseases. Some biochemical parameters like (glucose, urea, uric acid, creatinine, bilirubin, serum protei

The current study included measuring the percent of protein in the extract of nematode Ascaridia galli that infect chickens, it was 1.157% and equivalent to 11.570 mg /L., as well as the amino acid analysis in the nematode A.galli by using a high-performance liquid chromatography technique (HPLC), as was detect five types for amino acids in this extract Leucine, Threonin, Serine, Methionine and Valine as the amount of these amino acids in the extract was as follows 132.973, 26.994, 10.453, 2.243 and 1.888 mg /L., respectively, and other amino acids which Glutamic, Histidine and Tyrosin did not exist in the nematode A.galli.

Islamic banks are distinguished by providing banking activities that are unique in providing them from the rest of the other types of banks, and these activities are a group of banking services provided by the bank to its customers, whether these banking activities are tangible or intangible. At the same time, it is a source of bank profits, as Islamic banks impose a percentage of Islamic Murabaha on those banking activities , However, these banks have developed new services that they provide with the funds of the Central Bank initiative launched at the beginning of (2016) due to the economic conditions that befell the country due to the (financial security) crisis that the country faced in 2014. To put forward initiatives, and a

The present study deals with the websites of Iraqi political parties on the internet to identify the effectiveness in providing communicative applications that help audience to participate, express their opinions, their positions, and other aspects reflecting the extent of employing modern technological tools to allow opportunities for political, and democratic participation since the internet has become an effective tool for political communications of political parties. The research sample includes eight political parties. The research concludes that the Iraqi political parties do not employ interactive communication patterns to reflect their interests in communicating with the public, providing opportunities for their participation an

Tax revenues are considered one of the important sources of public revenues for the state as one of the tributaries that finance the public treasury to implement development plans. Real estate taxes are one of the sources of obtaining tax revenues in the state, as it follows that there are a number of factors that affect these revenues, which requires the development of necessary solutions and recommendations to address the resulting effects. Accordingly, this research sheds light on tax revenues in general and real estate tax revenues in particular to indicate the extent of their contribution to the total tax proceeds, as the tax proceeds of the real estate tax were analyzed into the total tax proceeds for the years (2017-2021). A numbe

The research aims to identify the current (after the readings in the collection of foreign
students to the geographical material) To achieve this, the researcher developed the following
null hypothesis:
No statistically significant differences at the level of (0.05) between the average scores who
are studying the use of article readings and the average external degree students who are
studying material in the traditional manner of collection.
The researcher has chosen Qsidia middle school Amma, which includes six divisions for
Grade average, randomly selected Division (a) to represent the control group, while
representing the Division of (c) the experimental group and reached the research sample (44)
student, b

Abstract. This study gives a comprehensive analysis of the properties and interactions of fibrewise maximal and minimal topological spaces. Fibrewise topology extends classical topological concepts to structured spaces, providing a thorough understanding of spaces that vary across different dimensions. We study the basic theories, crucial properties, and characterizations of maximal and minimal fibrewise topological spaces. We investigate their role in different mathematical contexts and draw connections with related topological concepts. By providing exact mathematical formulations and comprehensive examples, this abstract advances the fields of topology and mathematical analysis by elucidating the unique properties and implications of fib

This study seeks to identify the role that the leadership trend plays in the management of health institutions in Iraq and its impact on improving the quality of the health service provided by analyzing some opinions of affiliates working in the Iraqi health sector where a survey list was used as a main tool for collecting primary data, as it was subjected to this analysis ( 60) of the medical staff, of whom (40) are doctors and (20) are affiliated with the rank of assistant physician, and (60) members of the administrative cadre have undergone their various job ranks and administrative specializations (department manager, auditor, observer, accountant, statistician, secretary). Reliance on statistical software (spss) in data ana