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 .

To describe changes in attitudes and expectations of labor over the previous six decades, comparing the Iraqi generation who labored at home without medical assistance with their descendants.

Background: Friedreich ataxia (FRDA) is the most common form of inherited ataxia, comprising one-half of all hereditary ataxias with a carrier rate between 1 in 60 to 1 in 90 and with a disease prevalence of 1 per 29,000. It can occur in two forms the classic form or in association with a vitamin E dependent ataxia. The precise role of Vitamin E in the nervous system is unknown; An Oxidative attack is suspected to play a role in Ataxia with Vitamin E deficiency, as well as in Friedreich ataxia. Vitamin E is the major free-radical-trapping antioxidant.

Objective: Theobjectives of the study is to asses vitamin E level in patients with Friedreichs ataxia phenotype in Iraqi patients.

Background: Background : Patients with non-rheumatic atrial fibrillation have high risk of thromboembolism especially ischemic stroke usually arising from left atrial appendage .Transoesophageal echocardiography provides useful information for risk stratification in these patients as it detects thrombus in the left atrial or left atrial appendage. Objective : This study was conducted at Al-Kadhimiya Teaching Hospital to assess the prevalence of left atrial chamber thrombi in patients with chronic non-rheumatic atrial fibrillation using transoesophageal echocardiography and its clinical significance as well as to verify the superiority of transoesophageal over transthoracic echocardiography in the detection of these abnormalities. Type of

Results of charge, neutron and matter densities and related form factors for one- proton halo nucleus ⁸B are presented using a two- frequency shell model approach. We choose a model space for the core of ⁷Be different from that of the extra one valence proton. One configuration is assumed for the outer proton to be in 1p_1/2 - shell. The results of the matter density distributions are compared with those fitted to the experimental data. The calculated proton and matter density distributions of this exotic nucleus exhibit a long tail behavior, which is considered as a distinctive feature of halo nuclei. Elastic electron scattering form factors of this exotic nucleus are also studied. The effects of

Let R be a commutative ring with non-zero identity element. For two fixed positive integers m and n. A right R-module M is called fully (m,n) -stable relative to ideal A of , if for each n-generated submodule of Mm and R-homomorphism . In this paper we give some characterization theorems and properties of fully (m,n) -stable modules relative to an ideal A of . which generalize the results of fully stable modules relative to an ideal A of R.

    Keeping the secret itself of topics for values ​​are positive attribute of personality traits balanced. Objective of this research study of  Keeping the secret when spouses, the study of the theory based on the research and literature that dealt with the subject study is important to mention that there was no study of one Iraqi addressed the study of  Keeping the secret when spouses.

The researcher found the importance of the study of it's Keeping the secret when spouses. the factors that affect family relationships in terms of the stability of the marital relationship and this is reflected positively on the lives of family and community.