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 .

God Almighty put in his great book secrets that do not end, and wonders that do not expire, for he is the one from which the scholars are not satisfied, and he does not create due to the multitude of response, and it is the comprehensive and inhibitory book that God conceals to the worlds, and he challenged the two heavyweights to come up with something like it.

At all times, issues arise in the Noble Qur’an that fit the needs of the people of that time and their culture, for it is an eternal book, characterized by the ability to give, extend and respond to addressing the problems of the age and its variables, when the Arabs had little luck at the time of the message’s descent from the scientific culture, and their proficienc

This research aims to identify the role that forensic accounting plays on the transparency and quality of the financial statements in trade bank of Iraq and the Gulf Commercial Bank in Babylon. This research came to address the problem that most financial institutions suffer from, which is represented by the lack of transparency and the quality of the financial statements issued in a manner. Annual also the manipulation and fraud in the financial data, which causes a big gap between that institutions and organizational stakeholders. According to the implementation of the research hypothesis and the objectives of the research, a questionnaire was prepared consisting of three axes, the first axis dealing with the demographic distri

The research problem stems from a chief question: “What is the nature of the responsibility that «Al-Sabah Al-Jadeed» and «Al-Mada» Newspapers have undertaken in promoting the values of citizenship and national belonging in the society? The research aims to achieve a number of goals, including: Determining the most prominent themes that were emphasized in the opinion articles in these two newspapers within the framework of the responsibility of promoting the values ​​of citizenship and national belonging in society, and revealing the most prominent topics that were discussed in opinion articles in the two sample newspapers regarding the promotion of the mentioned values. This research is a desc

Water produced from power plants is one of the most important sources of water pollution, especially for areas like Baghdad, Contaminated industrial wastewater is a major environmental challenge due to the rapid growth of industries, leading to increased accumulation of harmful pollutants in water resources, the work is intended to study the impact of water generated from a power plant in the south on the level of heavy metals before and after the treatment process and after its discharge to the Tigris River. Objective is to determine the extent of heavy metals such as iron, copper, chromium, and zinc concentration in water extracted from various points and subsequently study the monthly variations of these elements with a view to assessmen

In this study, plastic wastes named (PET and PVC) were used to prepare polymer matrix composite (PMC) which can be used in different applications. Composite materials were prepared by mixing unsaturated polyester resin (UP) with plastic wastes, two types of plastic waste were used in this work included polyethylene-terephthalate (PET) and Polyvinyl chloride (PVC) with various weight fractions (0, 5,10,15, 20 and 25%) added as a filler in flakes form. In this work, some of the tests that were carried out included (tensile, bending, and compressive strength) as mechanical tests, in addition to (thermal conductivity and water absorption) as physical tests. The values of tensile, compressive strength and Young's modulus of UP increased after

Background: The novel coronavirus disease (COVID-19) is caused by Severe acute respiratory syndrome coronavirus 2 (SARS-Cov2) which utilizes angiotensin converting enzyme2 (ACE2) to invade the host cells. This membrane-bound peptidase is widely distributed in the body; its activity antagonizes the renin-angiotensin-aldosterone system (RAAS). Once SARS-Cov2 enters the cell, it causes downregulation of ACE2, resulting in the unopposed activation of RAAS. The unregulated activity of the RAAS system can deteriorate the prognosis in COVID-19 patients. A soluble form of ACE2 (sACE2) was reported to have a role in the SARS-Cov2 invasion of the susceptible cells.

Aim of the study: This study aims to inve

The research aims to achieve proof of convergence between optimal costs and standard costs in calculating costs for the economic unit, support efforts aimed at adopting optimal costs in cost accounts and accounting thought in general, and achieve benefit from the theory of convergence between optimal costs and standard costs in the field of achieving actual costs in The economic unit in order to reduce and converge, and this came to address the possibility of adopting the concept of optimal costs in the production costs calculations for the purposes of rationalizing administrative decisions, and rationalizing the preparation of financial statements within management accounting.

The research concluded that

The study aims at  evaluating  the penalty of  semi- intentional killing felony in the Egyptian and Algerian criminal law following the Islamic Law (Shari'a). The  study used the descriptive, evalutive and analytical  methodology  to  reach the topic in question. To meet the theoretical significance of the study, much data has been collected to give a comprehensive picture about the topic under examination. As for the practical significance of the study, it helps the juridical power to reconsider and phrase the legal materials of the semi-intentional killing penalty based on the Islamic law. The study has come to the conclusions that the Islamic Law (Shari'a) imposes a compensation (blood-money) to be g