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 aims to show the relationship between artificial intelligence in accounting education and its role in achieving sustainable development goals in the Kingdom of Bahrain. The research dealt with the role of artificial intelligence applications in accounting education at the University of Applied Sciences as a model for Bahraini universities to achieve sustainable development goals. The application of artificial intelligence in accounting education achieves seven of the seventeen sustainable development goals. It also concludes that there is an artificial intelligence infrastructure in the Kingdom of Bahrain, as it occupies a leading regional position in digital transformation, as Bahrain ranks first in the Arab world i

This study examines patterns of exposure of Iraqi university students to selective daily Iraqi newspapers and the motives of this exposure, as well as its associated factors that affect the average exposure. It tries to answer several questions, including those related to the levels of exposure of Iraqi university students to daily Iraqi newspapers and classification of patterns of selective exposure to daily Iraqi newspapers and the most prominent Iraqi daily newspapers that are selectively exposed by Iraqi university students. It also examines the motives of this selective exposure and factors that increase the degree of exposure to the daily Iraqi newspapers, and the most prominent stages in which Iraqi university students find their

The solvent free oxidation of benzyl alcohol was conducted employing Au and Pd supported catalysts, while utilizing hydrogen peroxide 35% (H2O2) as the oxidant, H2O2 is  very cheap, mild, and an environment friendly reagent, which produced water as the only by-product. Various proportions of Au-Pd catalysts on carbon and titanium oxide activated as supports were synthesized through the use of sol immobilization catalyst synthesis technique. Characterization of the synthesized catalysts was performed using X-Ray Diffraction (XRD), Brunauer-Emmett-Teller (BET), Field Emission Scanning Electron Microscopy (FESEM), and Transmission Electron Microscopy (TEM). It was found that the synthesized Au-Pd/ activated carbon catalyst was  benef

Colorectal cancer is a malignant condition that can arise from multiple causative factors. It ranks second, behind lung cancer, as a leading cause of cancer-related deaths worldwide. Extensive research has been conducted to unravel the genetic underpinnings and molecular mechanisms underlying the development of colorectal cancer (CRC). However, epigenetic modifications of histones at the DNA level have become significantly involved in several malignant diseases such as CRC. Hence, this research sought to assess, for the first time locally, the immunoexpression of HDAC-1 and 3 in a group of colorectal patients. Additionally, we explored potential correlations between the expression of HDAC-1, 3 and VEGF. This retrospective study enco