Volume 9 • Issue 1 • PP: 31-37 • 2023
On Orthogonal Reverse α-Derivations of Semi-prime -Ring
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In this paper, the concept of reverse a-derivation on G-ring M, and some results concerning two reverse a-derivations on M that are related to classical result of E.Ponser are presented. These results shows that if M is a2-torsion free semiprime G-ring, d and g are non-zero reverse derivations of M, then dg are not a non-zero derivation. The new main results present and study notion of orthogonally reverse a-derivations of M.
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References
[1] M.Ashraf and M.Rashid Jamal, “Orthogonal Derivation in G-Rings”, Advance in Algebra, Vol.3, No.1, pp.1-6, 2010.
[2] W.E.Barnes, “On The G-Rings of Nobusawa”, Pacific J.of Math., Vol.18, No.3, pp.411-422, 1966.
[3] M.Bresar and J.Vukman, “Orthogonal Derivation and an Extension of a Theorem of Posner”, Radovi Mathematics, Vol.5, pp.237-246, 1989.
[4] Bresar, M. and Vukman, “On Some Additive Mappings in Rings with Involution”, Aequations Math., Vol.38, pp.178-185, J.1989.
[5] J.C.Change, “a-Derivation with Invertible Values”, Bulletion of the Intitite of Math. Acad.Sinica, Vol.13, 1985.
[6] F.J.Jing, “On Derivations of G-Ring”, QUFU Shi Fan Daxue Xuebeo Ziran Kexue Ban, Vol.13, No.4, pp.159-161, 1987.
[7] A.H.Majeed, “On Orthogonal Reverse Derivations of Semiprime Rings”, Iraqi Journal of Science, Vol.50, No.1, pp.84-88, 2009.
[8] N.Nobosawa, “On a Generalization of the Ring Theory”, Osaka J. Math., Vol.1, pp.81-89, 1964.
[9] M.A.Ozturk, M.Sapanci, M.Soyturk and K.H.Kim, “Symmetric bi-Derivation on Prime Gamma-Rings”, Sci.Math., Vol.3(2), pp.273-281, 2000.
[10] H.J.Thahab, “On The Orthogonal a-Derivations of Semiprime G-Rings”, M.Sc. Thesis, Department of Mathematics, College of Education, Al-Mustansiriya University, 2013.
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