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Galoitica: Journal of Mathematical Structures and Applications

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Galoitica: Journal of Mathematical Structures and Applications

Volume 9 , Issue 1 , PP: 31-37, 2023 | Cite this article as | XML | Html | PDF

On Orthogonal Reverse α-Derivations of Semi-prime -Ring

Mudheher Abdul-Jabbar H. Albayati 1 *

  • 1 Faculty of Administration and Economics, Economics department, University of Misan, Iraq - (mudher68irri@yahoo.com)

    • Doi: https://doi.org/10.54216/GJMSA.090103

    Received: April 18, 2023 Revised: July 10, 2023 Accepted: October 28, 2023
    Abstract

    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.

    Keywords :

      , Prime, semiprime , G-ring, derivation , a-derivati , n, reverse a-derivati , n, orthogonal  ,   ,   ,   , reverse a-derivation.

    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.

    Cite This Article As :
    Mudheher Abdul-Jabbar H. Albayati. "On Orthogonal Reverse α-Derivations of Semi-prime -Ring." Full Length Article, Vol. 9, No. 1, 2023 ,PP. 31-37 (Doi   :  https://doi.org/10.54216/GJMSA.090103)
    Mudheher Abdul-Jabbar H. Albayati. (2023). On Orthogonal Reverse α-Derivations of Semi-prime -Ring. Journal of , 9 ( 1 ), 31-37 (Doi   :  https://doi.org/10.54216/GJMSA.090103)
    Mudheher Abdul-Jabbar H. Albayati. "On Orthogonal Reverse α-Derivations of Semi-prime -Ring." Journal of , 9 no. 1 (2023): 31-37 (Doi   :  https://doi.org/10.54216/GJMSA.090103)
    Mudheher Abdul-Jabbar H. Albayati. (2023). On Orthogonal Reverse α-Derivations of Semi-prime -Ring. Journal of , 9 ( 1 ), 31-37 (Doi   :  https://doi.org/10.54216/GJMSA.090103)
    Mudheher Abdul-Jabbar H. Albayati. On Orthogonal Reverse α-Derivations of Semi-prime -Ring. Journal of , (2023); 9 ( 1 ): 31-37 (Doi   :  https://doi.org/10.54216/GJMSA.090103)
    Mudheher Abdul-Jabbar H. Albayati, On Orthogonal Reverse α-Derivations of Semi-prime -Ring, Journal of , Vol. 9 , No. 1 , (2023) : 31-37 (Doi   :  https://doi.org/10.54216/GJMSA.090103)

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