Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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ON ORTHOGONAL REVERSE DERIVATIONS OF SEMIPRIME SEMIRINGS

  • Kim, Kyung Ho (Department of Mathematics, Korea National University of Transportation)
  • Received : 2022.02.26
  • Accepted : 2022.06.01
  • Published : 2022.06.30
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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.
  2. M. Chandramouleeswaran, V. Thiruveni, On derivations of semirings, Advances in Algebra 3 (1) (2010), 123-131.
  3. J. S. Golan, Semirings and their applications, Kluwer Academic press, (1999).
  4. E. Posner, Derivations in prime rings, Proc. Amer. Math. Soc. 8 (6) (1957), 1093-1100. https://doi.org/10.1090/S0002-9939-1957-0095863-0
  5. M. Samman, N. Alyamani, Derivations and reverse derivations in semiprime rings, International Mathematical Forum. 2 (39) (2007), 1895-1902. https://doi.org/10.12988/imf.2007.07168
  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.
  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. https://doi.org/10.1090/S0002-9904-1934-06003-8