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 .

Pregnancy pose an additional burden on the body of the mother so as to meet their needs and the needs of the fetus and the body's need to iron increases excessively during pregnancy and iron is an essential element for the formation of hemoglobin blood Either hemoglobin is the key ingredient for red blood cells which carries oxygen to parts of the body, alas, most of the pregnant women begin their pregnancy inadequate stocks of iron in their bodies, which does not cover their need and requirement of the fetus, especially in the second and third trimesters of pregnancy When you reach the mother to the period in which they did not have the adequate amount of iron to produce hemoglobin become the mother was anemic So emerged the problem of

This research aims to clarify the role of Information Technology Competency (ITC) with dimensions' (IT Usage, IT Knowledge, and IT Operations) as an independent variable in the activation of Human Resources Management Practices (HRM Practices) as a dependent variable with dimensions' (Training and Development, Recruitment, Job Design, and Performance appraisal). Based on this, the correlation and effect relationships between the independent and dependent variables are determined by formulating two main hypotheses. There are a significant relationship and effect of IT competency with HRM practices within the dimensions. Furthermore, the scope and population of this research are the Informatics and Communications P

The aim of this study was to assess the effectiveness of listening to music or Quran in reducing cancer patients’ anxiety before chemotherapy administration. Reducing anxiety in people with cancer, prior to chemotherapy administration, is a crucial goal in nursing care.

The research aimed to achieve many objectives represented in two variables, which are the impacted factors and the aggregate planning alternatives of workforce in Educational Al- yarmouk Hospital , This research started from a problem focused on finding solutions to the demand’s  fluctuation  or the energy limitation while the study importance is emerged from diagnosis the suitable strategy and adopt the suitable alternatives due to their importance in meeting the demand for the health service submitted by the hospital .This study  based on choosing assumptions of connection relationship and the impact among the mentioned variables in the(surgery and internal diseases) departments. The research is dependent on ch

The inhibitive action of Reactive Red (RR31) dye against corrosion of carbon steel in 1M acetic acid solution has been studied using gravimetric method at temperature ranged (288-318)K. The antibacterial activity for the different concentrations of RR31 dye against different bacterial species was studied. The experimental data indicates that this dye acts as a potential inhibitor for carbon-steel in acetic acid medium and the protection efficiency increase with increasing (RR31) dye. The adsorption of (RR31) dye on the carbon steel surface was found to follow Langmuir adsorption isotherm. Thermodynamic data for the adsorption process such as Gibbs free energy change ∆Gads, enthalpy change ∆Hads, and entropy change ∆Sads were estima

This research aims to study the contribution of social costs contribution to achieving social luxury in Al-Furat General Chemical Industries company that has considered second largest contamination in the area after the invasive power  to deal with chemicals in manufacturing and very dangerous to individual society and environment ,this is first to play an effective role by the senior parties related to sense of social responsibility of the internal and external environment of the company to identify costs that are preventing ,reduced and treating damage caused and achieving sustainable development ,to achieve this goal  and what they reached are the difficulty of accounting for the environment and social costs from final accou

The olive tree, has been used it is important plant for the time being some of their parts on a large scale in the treatment of gastrointestinal disorders and stimulate circulation . Moreover, it is used as antibacterial material and also to address some of the respiratory system, diabetes, food preservation osteoporosis. This study involved the collection of olive leaves from different areas in Baghdad / Iraq. These leaves have been harvested, wash it, then dried and crushed, where the study aimed to identify the active ingredients and chemical elements in the olive leaf as well as its effect on the action of GOT enzyme .The study showed that the aqueous extracts (cold and hot) of the olive leaves powder are acidic in nature pH values

The global oil market is one of the most important markets in the world and occupies especially for countries consuming and producing countries, and the status of understanding of the mechanism for determining prices in the market help to stand on many factors affecting oil demand and supply of oil and geopolitical factors, climate and alternative sources of energy .. etc. factors, and that the main objective of the research is to study the causes and results left behind by the oil price shocks in the world market, and the movement of these factors be through a cycle of energy that explain the strength of competition between these factors and their effects on prices, when demand increases evolution Large image leads to significan

Terrorism is a global phenomenon that engulfs most regions of the world to varying degrees. Media outlets are aware of the many incidents of violence and terrorism that have increased in recent times. The differences between the size of the phenomenon in different societies are the causes and severity of the phenomenon. On the role of local satellite channels in shaping the knowledge and trends of the Iraqi public towards the events of terrorism, in light of the assumptions of reliance on the media. The importance of this study is that it assesses the role of local satellite channels in the formation of knowledge and trends The study seeks to know the extent of exposure of the Iraqi public to local satellite channels, and to reveal the e