Korean J. Math. Vol. 30 No. 2 (2022) pp.341-349
DOI: https://doi.org/10.11568/kjm.2022.30.2.341

On orthogonal reverse derivations of semiprime semirings

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Published: Jun 30, 2022
Keywords:
Semiring, reverse derivation, semiprime, orthogonal, 2-torsion free
Mathematics Subject Classification:
16Y30, 06B35, 06B99

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KyungHo Kim
Department of Mathematics, Korea National University of Transportation, Chungju 27469, Korea

Abstract

 In this paper, we introduce the notion of orthogonal reserve derivation on semiprime semirings. Some characterizations of semiprime semirimgs are obtained by means of orthogonal reverse derivations. We also investigate conditions for two reverse derivations on semiring to be orthogonal.



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References

[1] M. Ashraf, M. R. Jamal, Othogonal derivations in Γ-rings, Advances in Algebra. 3 (1-2) (2010), 1–6. Google Scholar

[2] M. Chandramouleeswaran, V. Thiruveni, On derivations of semirings, Advances in Algebra 3 (1) (2010), 123–131. Google Scholar

[3] J. S. Golan, Semirings and their applications, Kluwer Academic press, (1999). Google Scholar

[4] E. Posner, Derivations in prime rings, Proc. Amer. Math. Soc. 8 (6) (1957), 1093-1100. Google Scholar

[5] M. Samman, N. Alyamani, Derivations and reverse derivations in semiprime rings, International Mathematical Forum. 2 (39) (2007), 1895–1902. Google Scholar

[6] N. N. Sulaiman, A. H. Majeed, Orthogonal derivations on an ideal of semiprime Γ-rings, International Mathematical Forum. 7 (25-28) (2012), 1405–1412. Google Scholar

[7] H. S. Vandiver, Note on a simple type of algebra in which cancellation law of addition does not hold, Bull. Amer. Math. Soc. 40 (1934), 914–920. Google Scholar