Let R be a Γ-ring and G be an R_Γ-module. A proper R_Γ-submodule S of G is said to be semiprime R_Γ-submodule if for any ideal I of a Γ-ring R and for any R_Γ-submodule A of G such that or which implies that . The purpose of this paper is to introduce interesting results of semiprime R_Γ-submodule of R_Γ-module which represents a generalization of semiprime submodules.

Interacting boson model version one has been used in the present

theoretical calculations. The energy levels & their transitions for dynamical  symmetry  0(6),  SU(3),  U(5),  ground-state  band,  Beta­ band, Gamma  band, B(E2), Ot, B(Ml), ,u,gt and  6(£2/Ml)have been  calculated  to  deduce  the  limit  of  Pt-198,  Z=78.  The  present results  confirmed  the  nuclear  behavior  of  this  isotope  lay  in  the

transitional region 0(6), SU(3) U(5). The calculations of 021 + & 022+

showed that the shape of this isotope is oblate according to Q21+  and pr

The investigation of determining solutions for the Diophantine equation  over the Gaussian integer ring for the specific case of  is discussed. The discussion includes various preliminary results later used to build the resolvent theory of the Diophantine equation studied. Our findings show the existence of infinitely many solutions. Since the analytical method used here is based on simple algebraic properties, it can be easily generalized to study the behavior and the conditions for the existence of solutions to other Diophantine equations, allowing a deeper understanding, even when no general solution is known.

The duo module plays an important role in the module theory. Many researchers generalized this concept such as Ozcan AC, Hadi IMA and Ahmed MA. It is known that in a duo module, every submodule is fully invariant. This paper used the class of St-closed submodules to work out a module with the feature that all St-closed submodules are fully invariant. Such a module is called an Stc-duo module. This class of modules contains the duo module properly as well as the CL-duo module which was introduced by Ahmed MA. The behaviour of this new kind of module was considered and studied in detail,for instance, the hereditary property of the St-duo module was investigated, as the result; under certain conditions, every St-cl

A   new   complex  of   Cr(UI)   has   been   prepared.  The   kinetics  and eqailibrium study of  the substitution reaction   for  the complex Trans­ KfCr(ox)z(H 0)2].3l--h0 {T I }, with 4-aminoantipyrine {AAP}, bave been per£Qrm d      in  aqueous  media   at  .(pH. = 4.9,   5.6 and 6.0)   (!!?0.4M NaN03).   Activation  pararrieters   for  the  reac(ions are  {Eat= l.89l  kCal

mor 1 ,        l:t=89.29  kCal  mo1"1  &nbsp

The study involved preparing a new compound by combining between 2-hydroxybenzaldehyde and (Z)-3-hydrazineylideneindolin-2-one resulting in Schiff bases and metal ions: Mn(II), Co(II), Ni(II), Cu(II), and Zn(II) forming stable minerals-based-Schiff complexes. The formation of resulting Schiff bases is detected spectrally using LC-Mss which gave corresponding results with theoretical results, 1H-NMR proves the founding of N=CH signal, FT-IR indicates the occurrence of imine band and UV-VIs mean is proved the ligand formation. On the other hand, minerals-based-Schiff was characterized using the same spectral means that relied with ligand (Schiff bases). Those means gave satisfactory results and proved the suggested distinguishable geometries.

The study involved preparing a new compound by combining between 2- hydroxybenzaldehyde and (Z)-3-hydrazineylideneindolin-2-one resulting in Schiff bases and metal ions: Mn(II), Co(II), Ni(II), Cu(II), and Zn(II) forming stable minerals-based-Schiff complexes. The formation of resulting Schiff bases is detected spectrally using LC-Mss which gave corresponding results with theoretical results, 1H-NMR proves the founding of N=CH signal, FT-IR indicates the occurrence of imine band and UV-VIs mean is proved the ligand formation. On the other hand, minerals-based-Schiff was characterized using the same spectral means that relied with ligand (Schiff bases). Those means gave satisfactory results and proved the suggested distinguishable geometries