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 identify the extent to which the media offices in the ministries depend on the website of the Iraqi Council of Ministers as a source of information. Such goal includes a set of sub-goals: Knowing the reasons for media offices' reliance on the information provided by the Cabinet's website; and revealing the benefit derived from relying on the Cabinet's website.

The researcher used the survey method to screen and comprehend the extent to which the media offices in the ministries depend on the website of the Iraqi Council of Ministers as a source of information.

The mechanism of comprehensive account of the limits of research wa

The objective of present study was to investigate the effect of using duplex volaticle oil of Rosmarinusoficinolis and Nigella sativain microbial quality, sensing and extending storage time of minced cold poultry meat. Duplex volaticle oil was added at 25, 50 and 75 mg/kg to minced poultry meat , these treatments were stored individually for (0 ,4 and 7) days at( 4-7) C0 . After making several microbial and sensing test. The following results were obtained:- The process of adding duplex volaticle oil of Rosmarinus officinolis and Nigella sativa to minced poultry meat led to significant reduced (P<0.01) in total arobic count, psychrophilic count and coliform bacteria during refrigerated storage periods. The results showed asignificant sens

The study aims to set an image to the mechanisms of the skills of the 21st century in the educational competencies of the basic education stage. To achieve this aim, a qualitative research design has been adopted in its analytical content analysis way. The study has arrived to the following conclusions:  the availability of: the communicative and team work skills with a percentage of 25.9%, linguistic competency with a percentage of 24.6%, the skills of local and global citizenship, creativity, and problem solving with a percentage of 13.6%, critical thinking with a percentage of 10.38%, technological culture with a percentage of 5.8%, pioneerism and initiativeness with a percentage of 10.38%, technological culture with a percentage of

The great  importance of training made it as an investment for the organization, and assert the Quality of performance which support it by prepare the employee to the Current and future Jobs . The Research problem a rounded about How to measure the impact of training based on (ISO 10015) and its effect on the Quality of performance , How to evaluation the results of training to attained the training goals . The Research aims to find out the effects of application of international standard guidelines (ISO 10015) to attained the quality of audit work achieved in the Federal Board of Supreme Audit. The Research sought to achieve a number of objectives cognitive and applied on the basis of four key assumptions, and other su

In this study; the genus of Sinoxylon Duftschmid, 1825 (Coleoptera, Bostrichidae) was revised. There were 3 species registered in our investigations: S. anale Lesne, 1897; S. ceratoniae (Linnaeus, 1758) and S. muricatum (Olivier, 1790), the last species was redescribed as being found for the first time for the Iraqi faunal insects. Key to the species were constructed and supported by figures of the main diagnostic characters and some morphological features.

Posible interference of vamin with the activity of several antibiotics against E. coli was evaluated in vitro. In MBS- glucose medium, significant growth delay was induced by 8 ug/ml of terramycin (oxytetracycline- polymyxin B) and bactrim (trimethoprim-sulphamethoxazole), and by 16 ug/ml of refocin, lincomycin, and chloramphenicol. Rapid growth inhibition was induced by 32 ug/ml of all an- tibiotic tested separately. Significant inactivation of up to 64 ug/ml of licomycin and bactrim was in- duced by the addition of vamin at a concentration of 1:20 v/v of the medium. This effect was found to be due to the presence of specific amino acids in vamin. Among them is valine, leucine, isoleucine tyrosine, tryptophan, phenylalanine, cysteine, meth

   Industrial Investment according to Clean Productive methods is an important element in the process of rational use of Economic Resources, and the Iraqi industrial sector relied on traditional production methods; the productive activities in this sector did not take into consideration the environmental dimension, which leads to achieving the optimal use of economic resources, so it was necessary to have new investment trends heading with Clean Production. Therefore, the research is based on the hypothesis that "Clean Production contributes to improving the environment and rational use of Natural Resources." Based on the descriptive - inductive analysis methodology that study of Iraqi industries with Clean Production,

 It is no doubt that dialogue is a behavior for human communication. It varies according to the place and occasion that requires it. Dialogues are of two types: positive purposeful and negative non-purposeful. The study aims to shed light on those patterns of dialogues contained in the Quranic stories represented by the characters and events participating in that dialogue activity. To expand the circle of social relations, and in order to make these relationships a success, there are several rules that must be adhered to.For instance, the dialogue should  not be tolerant to a personal opinion, or prolonged, or should not deviate from its text. The expression of polite dialogue has been raised in recognition of these dialogue et

Coupling reaction of 2-amino benzoic acid with phenol gave the new bidentate azo ligand. The prepared ligand was identified by Microelemental Analysis, FT-IR and UV-Vis spectroscopic technique. Treatment of the prepared ligand with the following metal ions (CoII, NiII, CuII and ZnII) in aqueous ethanol with a 1:2 M:L ratio and at optimum pH, yielded a series of neutral complexes of the general formula [M(L)2]. The prepared complexes were characterized using flame atomic absorption, (C.H.N) Analysis, FT-IR and UV-Vis spectroscopic methods as well as magnetic susceptibility and conductivity measurements. The nature of the complexes formed were studied following the mole ratio and continuous variation methods, Beer's law obeyed over a concentr