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 Qur'an is an inexhaustible source for researchers, and all of them find a rich material for its research, and no wonder in it is the book of the greatest Arabic. Quranic research has been an attempt to extract the secret in the miracle of the Koran, and not the Quranic miracle is limited to the word and its meaning, but that the miracle extends to include every sound in motion or silent; the sound performance of the Quranic text increases the meaning of beauty and earns the word heartbeat, Souls; and this may be due to the beauty of voice in the performance and harmony between sounds and words, and harmony between the exits and descriptions, or the tides of the tides,
Based on the above and to show the miraculous aspects of the Qu

Insurance actions has become a task of the vital foundations on    which the international economy depends, where its presence helped in the development of economic resources in which human resource is considered the most important of these resources. Insurance companies play the biggest role in protecting this resource and minimizing the impact of the dangers that verify this condition.Human has worked hard to get rid of the dangers and its harm, and to devise many ways to prevent them. A risk management is considered within human’s creations in order to create a society with fewer negative risks impacts.

                On this basis, th

In this research, the researchers attempted to reveal the non-verbal language in the Holy Qur'an through the hurt of the eye, its communicative effect, and its psychological significance in order to demonstrate the importance of this language. Fold the search ..

Administrative leaders conserned to understand the challenges which are faced their organizations and try to assimilate and adapt with the extent that achieves to it efficiency and effective- ess, and standing face to face to faceing any challenge.that threaten it’s existence thro- ugh using modern inputs reached to that level of these  challenges and applied the study on a sample deliberate random from teaching hospitals of the Directorate General for Health Baghdad Karkh, and the Directorate General for Health Baghdad Rusafa and the City of Medicine , The importance of t

The corrosion protection of low carbon steel in 2.5 M HCl solution by kiwi juice was studied at different temperatures and immersion times by weight loss technique. To study the determination of the optimum conditions from statistical design in evaluation of a corrosion inhibitor, three variables, were considered as the most dominant variables. These variables are: temperature, inhibitor concentration (extracted kiwi juice) and immersion time at static conditions.

These three variables are manipulated through the experimental work using central composite rotatable Box – Wilson Experimental Design (BWED) where second order polynomial model was proposed to correlate the studied variables with the corrosion rate o

Smoking-related diseases can be attributed to the inhalation of many different toxins, including heavy metals, which have a host of harmful health effects. The primary objective of this study was to determine whether local and imported cigarette brands used in Iraq , have they elevated levels of metals or not .Three metals Lead (Pb) , Cadmium (Cd) and Chromium(Cr) were determined in tobacco of seventeen brands of imported cigarettes commonly available in Iraq and three Iraqi domestic cigarettes , which were randomly taken from retail market in Baghdad by using flame atomic absorption spectrometry. The produced data of imported and local cigarette brands were discussed and compared together and with studies from elsewhere .The result

The research aims at identifying the organizational performance of the kindergarten teachers and defines the educational environment of kindergarten children. To achieve the objectives of the research, the researcher adopted the organizational performance scale for (Saadi, 2016), which was applied to kindergarten teachers. The scale consists of (43) paragraphs, and has good reliability and validity, as the coefficient of reliability (84.0) in a retest method, and (87.0) using the formula Alpha Kronbach. Additionally, the researcher adopted the educational environment scale for (Radam, 2015); the scale consists of (66) paragraphs, and it enjoys a good reliability and validity, as the coefficient of reliability (89.0) method of reliability

The research aims to measure the sustainability of the Iraqi economy for the period 1990-2018 as well as to show the impact of fluctuations in the level of GDP on financial sustainability, where financial sustainability is the necessary and sufficient condition for achieving economic and financial balance in the country, as financial sustainability reflects the movement of the state budget and its relationship to GDP through the indicators of deficit, fiscal surplus and public debt internal and external, as well as reflecting the art of managing public debt, and the more managed public debt is achieved, the more the management of public debt is achieved financial sustainability. for the state in the sense that there is a reciprocal