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Pure Mathematics for Theoretical Computer Science

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Pure Mathematics for Theoretical Computer Science
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Volume 4Issue 1PP: 12–17 • 2024

Orthogonal Semiderivations on Semiprime Γ-Semirings

Abdulrahman Hameed Majeed 1* ,
Sundus Taha Kathem 1
1Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq
* Corresponding Author.
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© 2024 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

Received: December 15, 2023 Revised: March 20, 2024 Accepted: May 28, 2024

Abstract

In this paper, we introduce the notion of orthogonal semi derivations on Γ-semi rings. Some characterizations of semiprime Γ-semirings are obtained by means of orthogonal semi derivations and obtained necessary and sufficient conditions for two semi derivations to be orthogonal.

Keywords

Γ-Semi rings Γ-Semi derivation prime Γ-semi rings Semi prime Γ-semi rings Orthogonal semi derivation

References

[1] N. Nobusawa, “On a generalization of the ring theory,” 1964.

[2] M. K. Sen, “Proceedings of the international conference on algebra and its applications,” 1981.

[3] D. H. Lehmer, “A ternary analogue of abelian groups,” American Journal of Mathematics, vol. 54, pp. 329–338, 1932.

[4] W. G. Lister, “Ternary rings,” Transactions of the American Mathematical Society, vol. 154, pp. 37–55, 1971.

[5] T. K. Dutta and S. Kar, “On regular ternary semirings,” Advances in Algebra: Proceedings of the ICM Satellite Conference in Algebra and Related Topics (World Scientific), pp. 343–355, 2003.

[6] M. M. K. Rao, “Γ-semirings—i,” Southeast Asian Bulletin of Mathematics, vol. 19, pp. 49–54, 1995.

[7] M. M. K. Rao, “Prime bi-interior ideals of Γ- semirings,” Journal of Hyperstructures, doi: 10.22098/jhs.2023.2525, vol. 11, no. 1, pp. 20– 30, 2022.

[8] J. Bergen, “Derivations in prime rings,” Canadian Mathematical Bulletin, vol. 26, pp. 267–270, 1983.

[9] M. Brešar and J. Vukman, “On some additive mappings in rings with involution,” Aequationes Mathematicae, vol. 38, pp. 178–185, 1989.

[10] M. Brešar, “Orthogonal derivations and extension of a theorem of posner,” Radovi Matematiˇcki, vol. 5, pp. 237–246, 1989.

[11] E. C. Posner, “Derivations in prime rings,” Proceedings of the American Mathematical Society, vol. 8, pp. 1093– 1100, 1957.

[12] J.-C. Chang, “On semi-derivations of prime rings,” Chinese Journal of Mathematics, pp. 255–262, 1984.

[13] C.-L. Chuang, “On the structure of semiderivations in prime rings,” Proceedings of the American Mathematical Society, vol. 108, pp. 867–869, 1990.

[14] A. Firat, “Some results for semi derivations of prime rings,” International Journal of Pure and Applied Mathematics, vol. 28, p. 363, 2006.

[15] S. Ali and M. S. Khan, “On orthogonal (σ, τ)- derivations in semiprime Γ-rings,” International Electronic Journal of Algebra, vol. 13, pp. 23–39, 2013.

[16] S. A. Hamil, “Commutativity of prime Γ-semirings with derivations and generalized derivations,” Journal of Physics: Conference Series, vol. 1804, p. 012091, 2021.

[17] M. K. Rasheed, F. A. Hameed, and A. H. Majeed, “On generalized (α,β) derivation on prime semirings,” Journal of Physics: Conference Series, vol. 1591, p. 012080, 2020.

[18] M. K. Rasheed and A. H. Majeed, “Developing an improved grey prediction model for application to electricity consumption prediction: Toward enhanced model accuracy,” Journal of Physics: Conference Series, vol. 1362, p. 012137, 2019.

[19] R. K. H. Ibraheem and A. H. Majeed, “On lie structure in semiprime inverse semirings,” Iraqi Journal of Science, pp. 2711–2718, 2019.

[20] K. K. Dey, A. C. Paul, and I. S. Rakhimov, “Semiprime gamma rings with orthogonal reverse derivations,” International Journal of Pure and Applied Mathematics, vol. 83, pp. 233–245, 2013.

[21] K. K. Sindhu, R. Murugesan, and P. Namasivayam, “Orthogonal semiderivations on semiprime semirings,” International Organization of Scientific Research Journal of Mathematics, vol. 11, pp. 18–24, 2015.

[22] B. Venkateswarlu, M. M. K. Rao, and Y. A. Narayana, “Orthogonal derivations on Γ-semirings,” Bulletin of the International Mathematical Virtual Institute, vol. 8, no. 3, pp. 543–552, 2018.

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Majeed, Abdulrahman Hameed, Kathem, Sundus Taha. "Orthogonal Semiderivations on Semiprime Γ-Semirings." Pure Mathematics for Theoretical Computer Science, vol. 4, no. 1, 2024, pp. 12–17. DOI: https://doi.org/10.54216/PMTCS.040103
Majeed, A., Kathem, S. (2024). Orthogonal Semiderivations on Semiprime Γ-Semirings. Pure Mathematics for Theoretical Computer Science, Volume 4(Issue 1), 12–17. DOI: https://doi.org/10.54216/PMTCS.040103
Majeed, Abdulrahman Hameed, Kathem, Sundus Taha. "Orthogonal Semiderivations on Semiprime Γ-Semirings." Pure Mathematics for Theoretical Computer Science Volume 4, no. Issue 1 (2024): 12–17. DOI: https://doi.org/10.54216/PMTCS.040103
Majeed, A., Kathem, S. (2024) 'Orthogonal Semiderivations on Semiprime Γ-Semirings', Pure Mathematics for Theoretical Computer Science, Volume 4(Issue 1), pp. 12–17. DOI: https://doi.org/10.54216/PMTCS.040103
Majeed A, Kathem S. Orthogonal Semiderivations on Semiprime Γ-Semirings. Pure Mathematics for Theoretical Computer Science. 2024;Volume 4(Issue 1):12–17. DOI: https://doi.org/10.54216/PMTCS.040103
A. Majeed, S. Kathem, "Orthogonal Semiderivations on Semiprime Γ-Semirings," Pure Mathematics for Theoretical Computer Science, vol. Volume 4, no. Issue 1, pp. 12–17, 2024. DOI: https://doi.org/10.54216/PMTCS.040103
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