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The Representaion of Algebraic Integers as Sum of Units over the Real Quadratic Fields: REPRESENTAION OF ALGEBRAIC INTEGERS AS SUM OF UNITS OVER THE REAL QUADRATIC FIELDS
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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 .

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Publication Date
Sat Feb 21 2026
Journal Name
Al-anbar University Journal Of Law And Political Sciences
The reasons for the fall of sanctions in the decisions and customs provisions in Iraqi law
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Publication Date
Mon Mar 08 2021
Journal Name
Baghdad Science Journal
the aspect of the radiation superposed on the soliton pulse propagated in single mode optical fiber
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the first part of the research involves investigate the aspect of the radiation superposed on the one bright soliton pulse propagated on ideal single mode

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Publication Date
Sat Feb 20 2021
Journal Name
International Journal Of Research In Social Sciences And Humanities
THE EFFECT OF THE ELECTRONIC ENVIRONMENT ON WORK ETHICS (APPLIED RESEARCH IN THE NATIONAL INSURANCE COMPANY)
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Publication Date
Sat Feb 01 2014
Journal Name
Journal Of Economics And Administrative Sciences
Evaluation the performance efficiency of the Public Manufacturing Sector in Iraq for the Period (2000-2009)
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The industrial production sector has an important role in the national economy of the advanced countries as well as the developing ones to get higher levels for their economy . We in Iraq , just like most of the develpoing countries , our economy still suffers of great shortage in this active sector in spite of the repeated statements about the desire of activating the contribution of this sector in the national economy . The industrial sector in Iraq suffers in general of many problems , especially the public industrial sector (manufacturing) . These problems have been  existed because of the unnatural conditions that Iraq has passed during the previous decades especially in the political and security sides . which reflecte

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Publication Date
Mon Feb 04 2019
Journal Name
Journal Of The College Of Education For Women
The Effectiveness Of the Poetic Text Between the Presence and Absence in Abu Firas al_Hamdani Romyate
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Abu Firas al- Hamdani is one of the most prominent abbasid poets Who characterized their poetry with high artistic quality especially in his Romyate which blended the quality of feelings of grief, sorrow, longing and nostalgia that makes sensitive self conflict that stems with time from one hand and with place on the other hand. Because we are dealing with a poet lived west spatial coercive which it has been hurt him within a time conflict swinging between despair and some times patience and hope other times between the present and his painful reality also between the past and the beautiful times.
This researcher is to stand on this Romyat by monitoring effectiveness of the poetic text based on conflict between the presenc

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Publication Date
Sat Feb 21 2026
Journal Name
Al–bahith Al–a'alami
Challenges Faced by the Media under the Fragile State: Analytical Study of the Iraqi Media Reality
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This study aims at defining the concept of the fragile state, a term that came into existence in 2014, when the states that had internal Problems and external interventions were referred to as the failure states. However, the indicators for their designation and the criteria adopted are 12 indicators that address all aspects of the State’s duties vis-a-vis its citizens. The study examined the reasons that led to the continuation of Iraq within the fragile states, and the selection of the five years within the time limits of the study due to the factors that led to the decline of Iraq and falling back within the most fragile countries. The study dealt with the fragile state challenges to the media reality as a result of the change of it

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Publication Date
Sun Apr 01 2018
Journal Name
Journal Of Economics And Administrative Sciences
The history of rational thought for the investment by human capital and the investing in it.
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The investment however "was its description and meaning, it remains a resident" in the composition of capital assets located in the forefront of the creation of productive assets, and this means that the investment in the productive sectors is a priority in achieving capital accumulation, on any other investment that takes place with the stages of advanced development of formation , not forgetting "to humans and investment humans as head of real money product, the source of the economic surplus and accumulation, and the source of producing values, and if human labor was the source of value, and the human was the source of work, therefore humanitarian work on different levels and skills presents capital", so the investment in huma

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Publication Date
Wed Sep 15 2021
Journal Name
Al-academy
The impact of e-learning on the cognitive level in the Corona crisis: أسماء غازي عبد
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E-learning is a necessity imposed by the Corona pandemic, which has disrupted various educational institutions in the world, but some of these institutions have not been affected and education has continued with them, due to their flexible educational system that was able to employ technology in the continuity of the educational process in the so-called e-learning, because It has characteristics that make it the most suitable alternative to avoid the consequences of the Corona pandemic and its damage to the educational process, as e-learning is one of the modern methods that contribute to enhancing the effectiveness of the learner, and enabling him to assume greater responsibility compared to traditional education, so the learner becomes

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Publication Date
Fri Dec 31 2021
Journal Name
Political Sciences Journal
The application of smart power in the regional power struggle in the Middle East after 2011
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Receipt date:12/7/2020 accepted date:24/1/2021 Publication date:31/12/2021

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

The constant characteristic of international relations is the constant change due to political, economic and military developments in addition to technology, and this in turn has led to many transformations in the concept of power, its uses, and the elements that form power and its distribution, and according to those variables, the concept of power has shifted from hard to soft, up to smart powe

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Publication Date
Tue Jun 30 2020
Journal Name
Journal Of Economics And Administrative Sciences
The impact of the empowerment strategy in the employees performance by mediating organizational trust (Field res
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The research aims to measure the impact of the empowerment strategy on the performance of employees by mediating organizational trust in the organization. The problem of research was the weak ability of most business organizations to employ the strategy of empowerment in maximizing the performance of employees, and the importance of research in practice lies in the results of a guide to managers in how to use the strategy of empowerment in maximizing the performance of employees by mediating organizational trust dimensions of ability, benevolence, integrity. In order to achieve the objectives of the research and to answer the questions of the problem, the researcher has adopted the descriptive analytical approach as the questionnaire was

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