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 .

Glorify and Praise be to God, and prayers and peace be upon the Messenger of God, his family, companions, and those who are loyal to him.

The subject derives its significance from two important sources , the first one lies in  the Sunnah of the Prophet, while the other is the family source , which enrich  this subject with great importance.

As for the objective of the topic, it shows to the reader the prophetic bases  that mitigate and  ease the burden of the husband in a way that secures the marital happiness, so that the Muslim woman takes it as a path  for her in life and a slogan that illuminates the darkness of the path and makes her to overcom

Agricultural companies could push investment forward and help in production base variation and developing production techniques. They also play a significant role in organizing and providing requirements of market economy. This work aimed at studying economic efficiency of the six agricultural companies that are registered at Iraqi stock market for the period 2005-2016. Capital of these companies was between (300 million-7.5 billion IQD). Several financial analysis indicators were applied such as activity percentages. Average of capital circulation was 0.91 for private company of agricultural production، and lowest share was for Iraqi company for producing and marketing field crops. Assets average circulation was highest for the pr

Government spending is the tool that the state uses to achieve its various goals. The research aims to identify the most important determinants of government spending in Iraq and to indicate the type and nature of the relationship between government spending and its determinants, which will contribute to understanding the movement of government spending. The results of the co-integration test using the border test methodology showed that the variables of population growth and oil prices have a long-term effect on government spending while inflation is not significant in the long run, and that 47% of the equilibrium imbalance (short-term imbalance) in government spending in the previous period (t-) can be corrected in the current period (t)

This study assesses the short-term and long-term interactions between firm performance, financial education and political instability in the case of Malaysia Small to Medium Enterprises (SMEs). The simultaneous insertion of financial education and political instability within the study is done intentionally to inspect the effect of these two elements in one equation for the Malaysian economy. Using the bound testing methodology for cointegration and error correction models, advanced within an autoregressive distributed lag (ARDL) framework, we examine whether a long-run equilibrium connection survives between firm performance and the above mentioned independent variables. Using this method, we uncover evidence of a positive long-term link b

The research aimed at measuring the degree to which the accept their class environment in governmental & civil Kindergartens &  it also aimed at knowing the differences between the dimensions of the measurement & the differences according to the kindergarten & class variables .

The researcher made a measurement for the class environment & it included five dimensions & the answering choices were three ( to a big extent , to some extent and no ) and after making sure that the measurement is usable , the researcher applied it on the sample which consisted of ( 212 )male & female children through the estimated answers of the teacher & the result was that there was an accep

The issue of volunteerism is one of the most important issues that have become prominent in social sciences and contemporary social thought, especially as a result of the transformations and changes that the world undergoes today. The voluntary sector has become the concern of all societies and governments for its development and service to society and various sectors. The practice of women is prominent in the work of volunteerism after 2003 in Iraq, but its work face a number of obstacles and hindrance. The problem of research is the obstacles of women's work in non-governmental organizations. The research aims to identify the nature and characteristics of volunteer work of Iraqi women.        &nb

It has been an increase concern of scientific and professional accounting sides on disclosure especially after appearance of business firms and accounting development with its relationship to financial statements which are considered to be outputs of the activity results.  The preparing of financial statements and auditing of those accounts according to normal principles and standards of accounting on both local and international levels. Accounting disclosure can be seen an importance through discover all fundamental and necessary information for proper supply. Therefore, the research will highlight on public companies commitment in Iraq for basis and standards which have taken disclosure in financial data. The conceptual frame of t