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 .

Abstract
        This research aims to identify the relationship and the impact of the behavior of organizational citizenship in the performance of employees, as practiced behaviors organizational citizenship substantial role in achieving the objectives of both the organization and its staff at the same time, so it affects a large extent on the characteristics and performance of individuals employees and thus influence the success of the organization as a whole, problem of the research has indicated that there is a clear failure in the study of the impact of the behavior of organizational citizenship in the performance of employees, was chosen

This work presents a design for a pressure swing adsorption process (PSA) to separate oxygen from air with approximately 95% purity, suitable for different numbers of columns and arrangements. The product refill PSA process was found to perform 33% better (weight of zeolite required or productivity) than the pressure equalization process. The design is based on the adsorption equilibrium of a binary mixture of O₂ and N₂ for two of the most commonly used adsorbents, 5A & 13X, and extension from a single column approach. Zeolite 13X was found to perform 6% better than zeolite 5A. The most effective variables were determined to be the adsorption step time and the operational pressure. Increasing the adsorption step

Receipt Date:10/11/2021 Acceptance Date:29/12/2021 Publication Date:31/12/2021

This work is licensed under a Creative Commons Attribution 4.0 International License.

The study aimed to clarify the conceptual explanations and the theoretical rooting of the concept of the populist phenomenon. And explore the political and cultural implications and connotations contained in populist political discourse. And to stand on the foundations and meanings on w

The research tagged with (similar rulings in the holy heavenly books - the Holy Qur’an and the Bible) highlights that there are a number of rulings in the heavenly books that are similar to each other in terms of content, meaning and significance and did not change from one prophet to another because they relate to the basic interests on which social relations are built. Documenting ties, preserving rights, preventing abuse, etc. These are among the divine purposes in clarifying rulings in order to reach their goals and achieve their goals. Therefore, by combining these rulings, many problems and incidents that are the subject of disagreement and doubt between the two religions can be achieved and addressed. Those who want reform, righ

Many studies mentioned that there is a decline in the a achievement of intermediate second class students in mathematics  . Parents and mathematics   teachers   had  emphasized   that  .  The  studies   related  this decline to the students weak attitude towards mathematics .

In spite  of the  importance  of this subject  , it has not been given enough attention  in research in our country . This research is an attempt to know  th e relationships  between  the  intermediate  second  class  students  , attitude and their achievement  in mathematics .

Also, to know the statistical sign

The aimed of the research was recognize the Big five personality factors and Academic procrastination among Baghdad university students, recognized differences between the gender according to   Big five personality factors and Academic procrastination , to recognized differences between specialization (scientific, human), and to recognize the relationship Between the variables of the research, and the extend of contribution Big five personality factors in Academic procrastination , to achieve these aims , Adopt scale to measure the Big five personality factors for (John Danahue & Kentle) , As we as the preparation of scale Based on An amber of previous scales to measure Academic procrastination, After processing the data st

Vocational education has great importance to comprehensive national development as it provides intermediate cadres able of operating the factories and laboratories in the farms and fields beside the work in the fields of health, service, administration and commercial. Due to the importance of this type of education in society, it is necessary to do a qualitative reform of vocational education in order to make the educational staffs get the necessary basic expertise to adapt the requirements of the labor market and try to rearrange and organize the workforce through put long-term economic and social policy through certain planning open to the workforce. The workforces structure according to gradual expansion in all the national ec

The present study aims to identify wisdom-based thinking and its relationship to psychological capital. It further aims to find out the differences in the level of wisdom-based thinking and psychological capital according to the variables of gender and specialization (scientific, humanities). To achieve this, the study has been conducted on a sample of (380) male and female students. The two scales, wisdom-based thinking and psychological capital are implemented to the sample after being constructed by the researcher and after ensuring their psychometric characteristics' suitability for the study's aims. Results concerning the first aim have shown that there is a significant relationship among students. The second aim has revealed that t