The purpose of this paper is to prove the following result: Let R be a 2-torsion free ring and T: R?R an additive mapping such that T is left (right) Jordan ?-centralizers on R. Then T is a left (right) ?-centralizer of R, if one of the following conditions hold (i) R is a semiprime ring has a commutator which is not a zero divisor . (ii) R is a non commutative prime ring . (iii) R is a commutative semiprime ring, where ? be surjective endomorphism of R . It is also proved that if T(x?y)=T(x)??(y)=?(x)?T(y) for all x, y ? R and ?-centralizers of R coincide under same condition and ?(Z(R)) = Z(R) .
Research summary
The researcher in theological sects finds that the controversial issues between the owners of the sects are many, filled with the books of the sects, articles and creeds, and when examining these books it became clear to us that the dispute is related, some of it is related to the meaning and some of it is related to the words and it is many, explained to us by rhetorical terminology such as guidance and delegation, Interpretation and others, and part of it is what is called the verbal disagreement, and sometimes it is by using common possible expressions of truth and falsehood, as in the saying of the Kharijites, “The judgment is only for God,” and some of it is related to something outside th
Let R be a ring and let A be a unitary left R-module. A proper submodule H of an R-module A is called 2-absorbing , if rsa∈H, where r,s∈R,a∈A, implies that either ra∈H or sa∈H or rs∈[H:A], and a proper submodule H of an R-module A is called quasi-prime , if rsa∈H, where r,s∈R,a∈A, implies that either ra∈H or sa∈H. This led us to introduce the concept pseudo quasi-2-absorbing submodule, as a generalization of both concepts above, where a proper submodule H of an R-module A is called a pseudo quasi-2-absorbing submodule of A, if whenever rsta∈H,where r,s,t∈R,a∈A, implies that either rsa∈H+soc(A) or sta∈H+soc(A) or rta∈H+soc(A), where soc(A) is socal of an
... Show MoreCdSe alloy has been prepared successfully from its high purity elements. Thin films of this alloy with different thicknesses (300,700)nm have been grown on glass substrates at room temperature under very low pressure (10-5)Torr with rate of deposition (1.7)nm/sec by thermal evaporation technique, after that these thin films have been heat treated under low pressure (10-2)Torr at (473,673)K for one hour. X-ray patterns showed that both CdSe alloy and thin films are polycrystalline and have the hexagonal structure with preferential orientation in the [100] and [002] direction respectively. The optical measurements indicated that CdSe thin films have allowed direct optical energy band gap, and it increases from (1.77- 1.84) eV and from
... Show MoreA study that collected 240 samples and divided into two groups: the first 120 samples were for diabetics and the second 120 samples were for healthy people, and each group included (90, 20.10) samples from the mouth, urine and vagina respectively, The results showed positive (28.67, 4.00, 1.67) isolates of Candida. In the mouth, urine and vagina, respectively, of diabetic patients compared to (9.33, 2.33, 5.00) positive isolates in the mouth, urine and vagina, respectively, in the healthy. The rate of positive isolates in women was high in women with diabetes and healthy, and it reached 25.33 and 9.00 isolates, respectively, compared with the rate of isolates in men with Candida disease for diabetic patients and healthy people 14.67 and 2.0
... Show MoreThis paper presents the synthesis and study of some new mixed-liagnd complexes containing nicotinamide(C6H7N2O) symbolized (NA) and phenylalanine (C9H11NO2)symbolized (pheH)] with some metal ions. The resulting products were found to be solid crystalline complexes which have been characterized by :Melting points, Solubility, Molar conductivity. determination the percentage of the metal in the complexes by flame(AAS), magnetic susceptipibility, Spectroscopic Method [FT-IR and UV-Vis]. The proposed structure of the complexes using program , chem office 3D(2006) . The general formula have been given for the prepared complexes :[M(NA)2(phe)]cl M(II): Mn(II) ,Co(II) , Ni(II) , Cu(II) , Zn(II) , Cd(II) & Hg(II) . NA = Nicotinamide= C6H7N2O Phe -
... Show MoreThis paper presents the synthesis and study of some new mixed-ligand complexes containing nicotinamide(C6H7N2O) symbolized (NA) and phenylalanine (C9H11NO2)symbolized (pheH)] with some metal ions. The resulting products were found to be solid crystalline complexes which have been characterized by :Melting points, Solubility, Molar conductivity. determination the percentage of the metal in the complexes by flame(AAS), magnetic susceptipibility, Spectroscopic Method [FT-IR and UV-Vis]. The proposed structure of the complexes using program , chem office 3D(2006) . The general formula have been given for the prepared complexes : [M(NA)2(phe)]cl M(II): Mn(II) ,Co(II) , Ni(II) , Cu(II) , Zn(II) , Cd(II) & Hg(II)). NA = Nicotinamide= C6
... Show MoreIn spite of economic importance of sugar cane and sugar beet as they described as industrial crops they still face decreasing rates of production and productivity in Iraq , and their production was not able to satisfy the local industrial demands for sugar . Thus this study aimed at studying and analyzing, production and productivity of sugar cane and sugar beet in Iraq and this has been done by using non serial data that can be obtained from official offices in Iraq . The area and production of sugar cane in Iraq recorded positive annual growth rates during 1970- 1978 which were 6% and 5% consequently , while the productivity of sugar cane recorded at the same duration of time negative annual growth rate which was 1% , while they recorded
... Show MoreTo investigate the effect of spraying some plant extraction and anti-oxidants on growth and yield of two cultivars of sunflower, a field experiment was conducted during fall season of 2009 and spring season of 2010 at the Experimental Farm, Department of Field Crop Science, College of Agriculture/ University of Baghdad. RCBD with three replications as factorial at two factors was used. First factor was cultivars Akmar and Shmoss, second was spraying with extraction of karkade at 25%, liquorices at 50%, vitamin C at concentration 1.5 mg.l-1 and nutrient which content 15 elements at concentration 15 % in addition to control treatment which sprayed with distilled water only. The result showed no significant differences between the two cultivar
... Show MoreThe new compounds synthesized by sequence reactions starting from a reaction of 4-hydroxybenzaldehyde with 1,5-dibromo pentane to produce dialdehyde)I( .Then compound )I( reacted with different aromatic amines to give schiff bases )IIIV(,thereafter added acetyl chloride to schiff bases to yield N-acyl derivatives)VVII(.While1,3-diazetine derivatives)VIII-X( were synthesized from the reaction of N-acyl derivatives with sodium azide.The reaction of thiourea with N-acyl compounds led to formation of thiourea derivatives (XI-XIII).Finally, the pyrimidine compounds )XIV-XVI( were synthesized by ring closure reaction of compounds(XIXIII) with diethyl malonate.The synthesized compounds were characterized by measurements of melting points,FTIR,1H-N
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