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 .

Importance of study :

The interesting of industrial sector and developing it after corner stone. It is important to build economic balanced and get behind and front linkage for transformative industrials, and this is important to get balanced.

The value of transformative industry sector is more important than other sectors in economy, and this is reflect the capital in industrial sector .Industry  sector is larger than other sectors ,so it regards the motive which moving the economic wheel .

The  problem :

The research treats reduction and retreat the ind

     This research aims to study the performance of operations to provide nursing services, which included dimensions (quality, timeliness, leadership skills, behavioral manifestations, relationships with others, problem-solving and decision-making, job performance) and its effects in nursing performance. The research to prove the value of the performance of service delivery processes dimensions by nursing staffs working in Iraqi hospitals, nursing and measuring performance. To find out the nature of nursing services, and a comparison between hospitals to measure the extent of the application dimensional among themselves, and that by relying on the dimensions of a global study, which was measu

The monetary policy is a vital method used in implementing monetary stability through: the management of income and adjustment of the price (monetary targets) in order to promote stability and growth of real output (non-cash goals); the tool of interest rate and direct investment guides or movement towards the desired destination; and supervisory instruments of monetary policy in both quantitative and qualitative. The latter is very important as a standard compass to investigate the purposes of the movement monetary policy in the economy. The public and businesses were given monetary policy signals by those tools. In fiscal policy, there are specific techniques to follow to do the spending and collection of revenue. This is done in order to

The study aims to identify the educational research obstacles as perceived by the faculty members at the universities of south in the west bank. As for study population, it included all (60) faculty-member in the colleges of education (bait lahem, alahliyah, al-khalil, and al-Quds almaftoha). To collect study data, the researcher used a questionnaire that consisted of (43) item; it has categorized into seven-domains: academic working conditions, academic management, resources and information, faculty members, publication, planning, and funding educational research. The findings revealed that Educational research obstacles were high with an average of (4, 39), no significant differences among sample averages and stander deviations on the

In this study, the results of the uranium concentrations and specific activity in 10 rice samples are described using a solid-state track detector (CR-39). Samples were collected from various local Iraqi markets with different origins (Iraq, India, America, and Thailand). Our findings found that the results of uranium concentration in all studied samples are ranging from (0.55 ± 0.28 to 1.74 ± 0.31) ppm with a weighted average of (1.24 ± 0.99) ppm. Also, results demonstrate that the specific activity values of the studied samples swing between values of (6.88 ± 3.52 and 21.49 ± 3.85) Bq/Kg. The obtained results of the studied rice samples are indicated that it is less than the acceptable limit of those studies established by ma

Background: Colorectal Cancer (CRC) is one of the most serious health problems and Herpes viridae may hasten the progression of colon cancer. Aim: The purpose of conducting this research is to investigate the existence of Herpes Simplex Virus (HSV1) infection in samples of Colorectal Cancer (CRC) compared with normal tissue. Material and Methods: 40 samples of tissues (30 patients ) with CRC, and (10 samples) of normal tissue (without cancer) were obtained, for immunohistochemically analysis of Herpes Simplex Virus (HSV1) expression Results: The results showed no significant data to justify the link between both Herpes Simplex Virus (HSV1) and human colorectal cancer. Despite of presence of Herpes Simplex Virus (HSV1) found in

A disease of the reproductive system known as "infertility" is characterized by the inability to conceive after twelve months or more of sexual activity. This study was carried out to investigate the level of the DAZ protein in “Azoospermia” Iraqi patients. One hundred and fifty human blood samples were collected from different regions in Baghdad governorate include (private medicals Labs and “high institute for infertility diagnosis” assisted reproductive techniques and Kamal Al- Samara'ay IVF Hospital). The control group (fertile) consists of 50 males with an age range between 22-51 years old, while the patient (infertile group) consists of 100 sample males with ages ranging between 25-51 years old. The correlation of mean age for

Polycystic ovarian syndrome, additionally called PCOS is the most widespread endocrine illness amongst women. The aetiology of PCOS is attributed to a multi-factorial interplay among environmental and genetic effects. The overarching goal evaluates the correlation among blood concentrations of total testosterone, sex-hormone-binding globulin (SHBG), estradiol (E2), follicle-stimulating hormone (FSH) and luteinizing hormone (LH) in ladies with PCOS and the impact of obesity, age, marital popularity on the obtained results. This study was conducted at the National Center for Educational Laborites /Medical City/ Baghdad. The study comprised of a sample of 83 women, elderly between 17 -45 years, who had been selected in a random manner

Controlling cost in construction projects is an essential issue. This study investigates the most critical problems that cause weakness in cost control in Iraqi construction projects. The quantitative technique was used by conducting a survey directed to professionals who work on construction projects. One hundred and sixty-four questionnaire forms were distributed to private sector companies, government companies, and government institutions, and the responses were subjected to the required statistical analysis. The results indicate that the most influential factors are the weakness in keeping up with the use of modern concepts, methods, and technologies, the delay in receiving the amounts due for work done from the owner, fluctuat