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 .

Religion in its general and simplified form is defined as a set of values or moral laws, which include provisions that people should follow to organize their affairs and ratify that they are provisions sent from the divine. 

      The concept of religion is not limited to the narrower sense represented by the performance of the virtual rituals of worship and religious fashions, etc., but also includes all the moral and spiritual values, conduct and good dealing that reflect the true essence of religion, which boils down to a set of values – such as sincerity, honesty and dedication to work, merciful dealing and compassion, etc. All religions agree on the moral content of religion. The Prophet of Is

The new multidentate Schiff-base (E)-6,6′-((1E,1′E)-(ethane-1,2-diylbis(azan-1-yl-1-ylidene))bis(methan-1-yl-ylidene))bis(4-methyl-2-((E)(pyridine-2-ylmethylimino)methyl)phenol) H2L and its polymeric binuclear metal complexes with Cr(III), Mn(II), Fe(II), Co(II), Ni(II), Cu(II), Zn(II), Cd(II) and Hg(II) are reported. The reaction of 2,6-diformyl-4-methyl-phenol with ethylenediamine in mole ratios of 2:1 gave the precursor 3,3′-(1E,1′E)-(ethane-1,2-diylbis(azan-1-yl-1ylidene))bis(methan-1-yl-1-ylidene)bis(2-hydroxy-5-methylbenzaldehyde) W. Condensation of the precursor with 2-(amino-methyl)pyridine in mole ratios of 1:2 gave the new N6O2 multidentate Schiff-base ligand H2L. Upon complex formation, the ligand behaves as a dibasic oct

The current study highlighted the violations and the steady depletion of , and agricultural and green areas in and around cities , which is an accurate scientific research problem that affects the future perspectives of these areas, their production and their consequences for the life of cities and their vital surroundings. This research took Baghdad city as a model of this critical phenomenon in order to study the reality of these regions, the size of violations, and to set a future concept and strategy, in addition to the proper treatment that preserves the assets of this great wealth , It was one of the most important conclusions Urban planning disruption of Baghdad city formations ,One of the most important recommendations , Scaling Bag

The role of the green areas lies in being one of the systems that plays the vital role in achieving the environmental dimension besides the socio-cultural body and the economic dimension in the hidden value of ecosystem services. However, many developing countries are characterized by a state of low community environmental awareness, which coincides with the basic need for land for housing and other uses, to take precedence over nature protection strategies. In the absence of clear planning and long-term planning strategies, all this led to abuses and violations of urban land use. In Iraq, the situation became more apparent due to the political, security and social conditions that followed the year 2003. Hence, the resea

The present study conducted to study epipelic algae in the Tigris River within Baghdad city for one year from September 2011 to August 2012 due to the importance role of benthic algae in lotic ecosystems. Five sites have been chosen along the river. A total of 154 species of epipelic algae was recorded belongs to 45 genera, where Bacillariophyceae (Diatoms) was the dominant groups followed by Cyanophyceae and Chlorophyceae. The numbers of common types in three sites were 47 species. Bacillariophyceae accounted 88.31% of the total number of epipelic algae, followed by Cyanophyceae 7.14 % and Chlorophyceae 4.55%. A 85 species (29 genera) recorded in site 1, 103 species (34 genera) in site2, 112 species (35 genera) in site3, 96 species

     This research examines the quantitative analysis to assess the efficiency of the transport network in Sadr City, where the study area suffers from a large traffic movement  for the variability of traffic flow and intensity at peak hours as a result of inside traffic and outside of it, especially in the neighborhoods of population with  economic concentration.                                                           &n