A submodule N is called rational in M if HomR( M N , E(M))=0, where E(M) is the injective hull of M. Rational submodules have been studied and discussed by many authors such as H.H. Storrer, H. Khabazian, E. Ghashghaei, A. Hajikarimi and A.R. Naghipour, M.S. Abbas and M.A. Ahmed. The main objective of this paper is to give a new class of submodules named P-rational submodules. This class is contained properly in the class of rational submodules. Several properties of this concept are introduced. The relationships between this class of submodules and some other related concepts are discussed such as essential and quasi-invertible submodules. Other characterizations of the P-rational submodule analogous to those which is known in the concept of the rational submodule are given.
Abstract
This work is considered the first study for the components of the Iraqi Leucaena leucocephala plant, where the different phytochemical compounds that present in the aerial parts were identified by using the gas chromatography/mass spectrometry technique (GC/MS). The type of the components and their concentration will differ according to the part of the plant used and the method of extraction (hot and cold). This study made a comparison in lupeol concentration that was identified and isolated from petroleum ether fractions of Leucaena leucocephala by using Gas Chromatography/Mass Spectrometry (GC/MS), High-performance thin-layer chromatography (HPTLC), and Preparative High-Performance Li
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The aim of this paper is introducing the concept of (ɱ,ɳ) strong full stability B-Algebra-module related to an ideal. Some properties of (ɱ,ɳ)- strong full stability B-Algebra-module related to an ideal have been studied and another characterizations have been given. The relationship of (ɱ,ɳ) strong full stability B-Algebra-module related to an ideal that states, a B- -module Ӽ is (ɱ,ɳ)- strong full stability B-Algebra-module related to an ideal , if and only if for any two ɱ-element sub-sets and of Ӽɳ, if , for each j = 1, …, ɱ, i = 1,…, ɳ and implies Ạɳ( ) Ạɳ( have been proved..
The effect of UV-light on the tensile properties of pure PC has been studied. It was shown that irradiation of PC undergo a drop in the tensile properties of 30 hour of exposure. The results of irradiated samples shows that the addition of ZnO and TiO2 with different percentages (0.5, 1, 1.5 %) will reduce the Young modulus and ultimate stress of PC/ZnO ,PC/ TiO2 composites
Age, hypertension, and diabetes can cause significant alterations in arterial structure and function, including changes in lumen diameter (LD), intimal-medial thickness (IMT), flow velocities, and arterial compliance. These are also considered risk markers of atherosclerosis and cerebrovascular disease. A difference between right and left carotid artery blood flow and IMT has been reported by some researchers, and a difference in the incidence of nonlacunar stroke has been reported between the right and left brain hemispheres. The aim of this study was to determine whether there are differences between the right and left common carotid arteries and internal carotid arteries in patient
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In this work lactone (1) was prepared from the reaction of p-nitro phenyl hydrazine with ethylacetoacetate, which upon treatment with benzoyl chloride afforded the lactame (2). The reaction of (2) with 2-amino phenol produced a new Schiff base (L) in good yield. Complexes of V(IV), Zr(IV), Rh(III), Pd(II), Cd(II) and Hg(II) with the new Schiff base (L) have been prepared. The compounds (1, 2) were characterized by FT-IR and UV spectroscopy, as well as characterizing ligand (L) by the same techniques with elemental analysis (C.H.N) and (1H-NMR). The prepared complexes were identified and their structural geometries were suggested by using elemental analysis (C.H.N), flame atomic absorption technique, FT-IR and UV-Vis spectroscopy, in additio
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