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 current research aims to know the complementary use of the paper book and the digital book by defining the paper book and the digital book and knowing the methods and methods of obtaining each of them and indicating the extent of their use and for what purpose and knowing the difficulties that researchers face in using each of them and which is better using the paper book or the digital book in preparing research Studies and for no reason. The research relied on the descriptive approach and the questionnaire as a tool for data collection, and it was distributed to professors and students of Iraqi universities. The research sample reached (219) individuals and reached a set of results, the most important of which are: Preference for the

The research problem can be summarized through focusing on the environment that surrounds students and class congestion, how these factors affect directly or indirectly the academic achievement of students, how these factors affect understanding the scientific material that the student receives in this physical environment, how classroom’s components such as seats, space With which the student can move, the number of students in the same class,  the lighting, whether natural or artificial, and is this lighting sufficient or not enough, the nature of the wall paint old or modern, is it comfortable for sight, the blackboard if it is Good or exhausted,  In addition to air-conditioning sets in summer and winter, this is on the on

The aim of the research is to measure the change in the impact of the factors of the Corona pandemic on psychological sensitivity and COVID-19 phobia in a sample of Bisha University students and to detect the differences in the phobia (phobia) Covid-19 among the sample members in the measurement before the ban and after the ban was opened, in addition to the differences in psychological sensitivity of  The sample has between sizes before and after the spread of the Corona pandemic, as well as the differences in them according to the gender variable (male, female). The researcher relied on the comparative approach. The scale of psychological sensitivity and COVID-19 phobia was applied to a sample of (62) male and female respondents.

The research tagged with (similar rulings in the holy heavenly books - the Holy Qur’an and the Bible) highlights that there are a number of rulings in the heavenly books that are similar to each other in terms of content, meaning and significance and did not change from one prophet to another because they relate to the basic interests on which social relations are built. Documenting ties, preserving rights, preventing abuse, etc. These are among the divine purposes in clarifying rulings in order to reach their goals and achieve their goals. Therefore, by combining these rulings, many problems and incidents that are the subject of disagreement and doubt between the two religions can be achieved and addressed. Those who want reform, righ

The energy consider generally and specifically the petroleum energy
from the prior requirement of the population and nations, and the basics of the
survival of mankind and all the challenges for the sake of continuum, so
without this energy the life of ankind being varied, so far the life is still as a
fact on the planet earth, and suppose the life may continue as the willing of
Allah ,that the events and the standards and the degree of development is still
as it is, in another word no any technical developments and no any
entertainment no transportation and also there is no demographic domination
for the whole lands belonging to Allah, certainly no way to talk more on what
we and the others knew, what is the g

This study was conducted in order to statement the effect of ginger (Zingiber officinale) extracts in reducing the presence of the bacterium Salmonella typhimurium in some foods products.
Qualitative disclosures effective chemical compounds (alkaloids, flavonoids, phenols, tannins, terpenes) showed that the extracts of ginger an effective compounds as follows: oil extract and fresh juice> aqueous extract warm> aqueous extract cold. And studied the impact extract of fresh ginger juice, hot water ,cold water and oil rates extracts (1,2,3)% in bacteria test has shown that all s of extracts clear impact inhibition has oily extract of ginger recorded the highest value to inhibition zone reaching 35 mm when the concentration of 3%, f

The Islamic Banks including the Iraqi ones are often resorted to support their governance frameworks in order to improve its competitiveness in their communities. Where, those banks are looking for activities that enhance their governance; one of these activities is Shariah Audit that provided the auditing capabilities to face of developmental challenges and increase competitiveness. Therefore, the content of this paper, discusses know-how to use the Shariah Audit and its references in support of the Shariah Governance in the Iraqi Isla

Internal control system is a safety valve that preserves economic units assets and ensure the accuracy of financial data, as well as to obligation in the laws, regulations, administrative policies ,and improve the efficiency, effectiveness and economic of operation, so it has become imperative for these units attention to internal and developed control system The research problem in exposure the economic units when the exercise of their business to many of the risks to growth or hinder the achievement of its objectives and the risks (financial, operational, strategy, risk) and not it rely on risk Assessment according to modern scientific methods, as in Brown's risk Classification, Which led to the weakness of the internal control identif