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Galoitica: Journal of Mathematical Structures and Applications

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Online: 2834-5568
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Galoitica: Journal of Mathematical Structures and Applications
Full Length Article

Volume 9Issue 1PP: 31-37 • 2023

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

Mudheher Abdul-Jabbar H. Albayati 1*
1Faculty of Administration and Economics, Economics department, University of Misan, Iraq
* Corresponding Author.
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© 2023 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

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

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

References

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[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.

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[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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Albayati, Mudheher Abdul-Jabbar H.. "On Orthogonal Reverse α-Derivations of Semi-prime -Ring." Galoitica: Journal of Mathematical Structures and Applications, vol. Volume 9, no. Issue 1, 2023, pp. 31-37. DOI: https://doi.org/10.54216/GJMSA.090103
Albayati, M. (2023). On Orthogonal Reverse α-Derivations of Semi-prime -Ring. Galoitica: Journal of Mathematical Structures and Applications, Volume 9(Issue 1), 31-37. DOI: https://doi.org/10.54216/GJMSA.090103
Albayati, Mudheher Abdul-Jabbar H.. "On Orthogonal Reverse α-Derivations of Semi-prime -Ring." Galoitica: Journal of Mathematical Structures and Applications Volume 9, no. Issue 1 (2023): 31-37. DOI: https://doi.org/10.54216/GJMSA.090103
Albayati, M. (2023) 'On Orthogonal Reverse α-Derivations of Semi-prime -Ring', Galoitica: Journal of Mathematical Structures and Applications, Volume 9(Issue 1), pp. 31-37. DOI: https://doi.org/10.54216/GJMSA.090103
Albayati M. On Orthogonal Reverse α-Derivations of Semi-prime -Ring. Galoitica: Journal of Mathematical Structures and Applications. 2023;Volume 9(Issue 1):31-37. DOI: https://doi.org/10.54216/GJMSA.090103
M. Albayati, "On Orthogonal Reverse α-Derivations of Semi-prime -Ring," Galoitica: Journal of Mathematical Structures and Applications, vol. Volume 9, no. Issue 1, pp. 31-37, 2023. DOI: https://doi.org/10.54216/GJMSA.090103
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