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 present analysis targets to recognize the influence of the separate teaching approach on the accomplishment of grammar for scholars of the College of Islamic Sciences. The target of attaining this target led the investigations developing the subsequent null theories: 1. No statistically substantial variance is happened at the consequence level of 0.05 between the mean scores of the scholars in the investigational category who learnt consistent with the separate learning approach and the mean scores of the scholars in the control category who learnt in the conventional method in the accomplishment test. 2. No statistically substantial variance has been observed at the consequence level of 0.05 in the mean differences between the

Authentic materials are the most important tools that the teacher could use in class in order to make teaching go smoothly and effectively in transmitting the necessary knowledge to all students. This research has investigated experimentally the effect of using authentic materials in teaching English as a foreign Language, because a number of studies point out that the use of authentic materials is regarded a useful means to motivate learners, arouse their interest and expose them to the real language they will face in real life situations.

It is hypothesis that there is no statistical significance difference between the experimental group who taught English as a foreign language by using the authentic materials with those  

This research aims to identify the reality of teaching political science research methods curriculum, to observe practices, and differences in teaching and learning between the Arab and Western universities. Moreover, it focuses on the difficulties that face students' acquisition of the course skills. The research uses the course model of some Western and Arab universities as case study.

This research shows that the curriculum do not reach yet the final form as other political science curriculums, and its upcoming changes will reflect the needs of stakeholders. The best method to teach this curriculum is to use applied learning in groups, learning by doing, and finally problem-based learning approach. Using optimal assessment deep

This research aimed to identify the structural model of the relationship between emotional creativity and self-efficacy among male and female students of the preparatory year at Tabuk University. The current study adopted the descriptive correlational approach, as it is appropriate to the nature of the study. The study tools contained (60) items that measure the relationship between emotional creativity and self-efficacy among the male and female students of the preparatory year at Tabuk University. The study sample was chosen by the stratified random method of the study community, where the study sample reached (183) male and female students of the preparatory year at the University of Tabuk. The results of the study showed that there a

The purposes of study are to measure the perceived competence and the locus of control among sixth-grade students, to identify the statistical differences between the perceived competence and the locus of control among sixth-grade students regarding the variable of gender, achievement, and economical status, and lastly, explore the correlation relationship between perceived competence and locus of control among sixth-grade students, To do this, the researchers have constructed two scales: one to measure the perceived competence based on bandura's theory (social-cognitive theory) which consisted of (26) items and the other to measure the locus of control based on Rotter's theory (social-learning theory) which included (25) items. The samp

The purpose of this research is to identify the effect of the use of project-based learning in the development of intensive reading skills at middle school students. The experimental design was chosen from one group to suit the nature of the research and its objectives. The research group consisted of 35 students. For the purpose of the research, the following materials and tools were prepared: (List of intensive reading skills, intensive reading skills test, teacher's guide, student book). The results of the study showed that there were statistically significant differences at (0.05) in favor of the post-test performance of intensive reading skills. The statistical analysis also showed that the project-based learning approach has a high

Technology plays a vital role in all walks of life, one of these is Education. Google Classroom is one of the educational tools that are free of cost and recently has gained popularity within a short period in many countries, including Iraq. The primary purpose of this study is to explore the Google Classroom use in EFL learners' composition writing. The sample of the study is EFL Second-year College students from the College of Science for Women /Computer Science Department, which consisted of (35) students who have implemented Google Classroom for at least one semester in their classroom. The students were asked to finish two uncompleted paragraphs that have the only main idea and write a suitable conclusion to each one. The results sh

               The present study aims at answering the following questions:.

1-Which is more effective in enriching students.  Vocabulary ,the use of short stories or the      traditional way?

2-What extent has the use of short stories an effect upon the students. achievement in           vocabulary test?

3- Is there any significant difference between the male and female student of the                    experimental group in vocabulary achievement test?

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