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 research aimed to know the effect of the Parashot strategy in developing the reading comprehension skills of first-grade intermediate students in reading. The researchers put the following two null hypotheses: There is no statistically significant difference at the level (0.05) between the average scores of the experimental group students who study the subject Reading with the Parashot strategy in the pre and post-tests in developing reading comprehension skills as a whole. There is no statistically significant difference at the level (0.05) between the average scores of the experimental group students who study the reading material using the Parashot strategy and the average scores of the control group students who study the same subje

publishing has become a large space in the field of interactive education and modern pages have become dedicated to the service of the educational effort in this area as the research in this context of the urgent scientific necessities, especially as we consider in Iraq from the new countries in the exploitation of these new technologies and investment possibilities of the information network And the contents of different in the framework of so-called distance education Here lies the problem of research in the possibility of finding scientific solutions for the design of interactive inter active website for students of the preparatory stage in Iraq and to find out the scientific ways to find design The study, which included the problem of

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

Many undergraduate learners at English departments who study English as a foreign language are unable to speak and use language correctly in their post -graduate careers. This problem can be attributed to certain difficulties, which they faced throughout their education years that hinder their endeavors to learn. Therefore, this study aims to discover the main difficulties faced by EFL students in language learning and test the difficulty variable according to gender and college variables then find suitable solutions for enhancing learning. A questionnaire with 15 items and 5 scales were used to help in discovering the difficulties. The questionnaire was distributed to the selected sample of study which consists of 90 (male and female) stud

Many undergraduate learners at English departments who study English as a foreign language are unable to speak and use language correctly in their post -graduate careers.  This problem can be attributed to certain difficulties, which they faced throughout their education years that hinder their endeavors to learn. Therefore, this study aims to discover the main difficulties faced by EFL students in language learning and test the difficulty variable according to gender and college variables then find suitable solutions for enhancing learning.  A questionnaire with 15 items and 5 scales were used to help in discovering the difficulties. The questionnaire was distributed to the selected sample of study wh