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 purpose of this study is to assess the level of moral development, spiritual intelligence, and critical thinking of nurses, and to see if there is a relationship between these constructs for them. A descriptive correlational design was used, with a sample of 102 nurses in Iran. The descriptive statistics and Pearson’s correlation were done on the survey results using SPSS (Version 24). The moral development level scores of the nurses were 34 ± 2.17, which is considered average, critical thinking was 25 ± 1.23, which is considered relatively high, and spiritual intelligence scores were 41 ± 2.75, which is considered relatively low. Both spiritual intelligence and critical thinking were positively correla

Abstract

In light of the great technological development and the emergence of globalization has increased global competition, where it became competitive exercise pressure on all sectors. In light of this companies mast enviorment depend on the means that keeps them on the competitive position through access to information about competitors in order to help them to draw a strategy that will achieve a competitive edge either through excellence or reduce the costs of their products and this means intelligence competitive and reverse engineering that help to gain information on competitors analyze and put of the decision-maker From this point formed the idea of ​​research in the statement of the role of

The present study cognitive aims to investigate the negation phenomenon in American political discourse under Critical Discourse Analysis (CDA) principles. The research sample includes two speeches given by Clinton and Trump in their election campaigns in 2016. Since the nature of the study follows the social-cognitive approach, the researcher adopted two models of analysis to achieve the study’s objectives: First, the theoretical framework of MST (developed by Fauconnier (1994), Fauconnier and Sweetser (1996) to examine meaning construction resulting from building different levels of negative mental spaces by two different genders the selected speeches. Second, pragmatic model to examine the role of gender from the functional per

Brainstorming is considered as one of the manners that develop learners' mental abilities. Besides, it can help learners get a lot of ideas and thoughts. And by following applied steps to answer the problem concerned, the researcher carried out this practical study aimed at:Developing the ideas of design of third year students/Institute of Fine Arts/Evening Studies- Baghdad/First Rusafa by employing Brainstorming mechanism to develop the ideas of design of institute students in designing the technical advertisement and to achieve the authenticity of the goal of the research, Department of Plastic Arts/Institute of Fine Arts/Evening Studies/Baghdad-First Rusafa was chosen as a case study for the research. It embraced (20) students who rep

Nowadays, the ideas of integrating the concepts of the environment and saving it are being famous. These ideas are widely seen in many fields of study, and language education is one of them. Thus, the identity of English Language teachers (ELT) is a step toward transferring this concept in EFL materials in ELT departments. The EFL teacher's identity takes different meanings. Sometimes, it only means the teacher who teaches the English language, and other times, it means, the cultural and social aspects that the teacher and students interact during the study course. These cultural and social aspects represent the environment in teacher’s identity. This study aims to explore the environmental identity within EFL teacher identity. The sam

The most influential theory of ‘Politeness’ was formulated in 1978 and revised in 1987 by Brown and Levinson. ‘Politeness’, which represents the interlocutors’ desire to be pleasant to each other through a positive manner of addressing, was claimed to be a universal phenomenon. The gist of the theory is the intention to mitigate ‘Face’ threats carried by certain ‘Face’ threatening acts towards others.

            ‘Politeness Theory’ is based on the concept that interlocutors have ‘Face’ (i.e., self and public – image) which they consciously project, try to protect and to preserve. The theory holds that various politeness strategies are used to prot

The scientific and practical importance of this study lies in analyzing the phenomena of commercial blocs as a means of managing the future struggle as Zbigniew Brzhenski in his book Our of Control which was translated into Arabic under the title of (chaos) in 1993. The most important phenomenon of the 21th century is the geopolitical phenomenon presented by the international blocs. That is, the new regime will be united in the form of economic blocs and political alliance. Consequently, the future struggle will be economic in nature under the chaos which the new order is living.  Under the retreat of the  economy that effected the industrial countries and the world countries which have become unable to treat the crisi