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 study aims at empirically investigating the effect of vocabulary learning strategies on Iraqi intermediate school students’vocabulary performance and reading comprehension. The population of the present study includes all the 1^st year male students of  Al-Wark’a intermediate  school of Al-Risafa 1/ General  Directorate of Education for the first course of the academic year (2015-2016). To achieve the aim of the study ,a pre-test and post-test after (5) weeks of experiment are administrated .The sample of the present study consists of (100) subjects :(50) students as an experimental group and other (50) students as  a control group . The subj

The research aimed to identify the causal relationship between forgiveness and psychological hardness for university students, by answering the following questions: Does forgiveness cause psychological hardiness? Does psychological hardiness cause forgiveness? Is the relationship between the two variables a reciprocal relationship? The research sample consisted of (300) male and female students from the universities of Baghdad and Al-Mustansiriya University. To extract the psychometric properties of the two scales: forgiveness and psychological hardiness, a sample of (50) male and female students employed to repeat the test, making the six connections between the two research variables. To determine the causal relationship, The Pearson c

The research aims to know the relation between positive thinking and self academic motivation, trend towards teaching profession. So a sample of (344) male and female student of the morning study of education colleges from the two universities of Baghdad and al Mustansria for the academic year 2012-2013.

So three tools had been used to achieve the procedures of the research which are: the scale of positive thinking constracted by Abdal satar Ibrahim year 2010, the scale of self academicmotivation constracted by (Gottfried) and adapted by Hanan Hussan year 2010, the scale of teaching profession trend constracted by Enayat Zaki year 1974.

And by using the statistical means of person

The aim of this research is to employ the roundhouse strategy to study its impact on the students achievement of the 10th grade in physics and their core thinking. After the application of the research experience and gaining data, which was processed statistically using the statistical packages program (SPSS). The results of the researcher revealed the superiority of the students of the experimental group who studied using the roundhouse strategy on the students of the control group who studied the usual method in the achievement test. As results showed that there were statistically significant differences between the average scores of the experimental group and the average scores of the control group students in the core thinking test and

The study aims to identify the students’ attitudes toward recent techniques’ use in teaching; using power point software and data show to facilitate teaching approaches as well as following the approach of lecture in giving subjects, do these techniques facilitate, increase, and tackle the difficulties of subjects, do these attitudes positive or negative?, and to what extent these techniques raise up students’ motivation.   

This study aims to investigate the degree of practicing the motivated classroom evaluation environment for learning and its relationship to different feedback patterns. To achieve the objectives of the study, the correlational descriptive research design was employed. A questionnaire was constructed consisting of two parts: the classroom evaluation environment (13) items, and feedback patterns (24) items on a five-point scale. The psychometric properties of the questionnaire were verified in terms of validity and reliability. The questionnaire was applied to a sample of (265) male and female teachers who work in the second cycle schools for grades (5-10) of basic education in all academic majors in the Governorate of Muscat in the Sultan

The research aims to know the impact of the innovative matrix strategy and the problem tree strategy in teaching mathematics to intermediate grade female students on mathematical proficiency. To achieve the research objectives, an experimental approach and a quasi-experimental design were used for two equivalent experimental groups. The first is studied according to the innovative matrix strategy, the second group is studied according to the problem tree strategy. The research sample consisted of (32) female students of the first intermediate grade, who were intentionally chosen after ensuring their equivalence, taking into several factors, most notably (chronological age, previous achievement, and intelligence test). The research tools con