Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
권호 표지
DOI QR코드

DOI QR Code

ON GENERALIZED DERIVATIONS OF PRIME RINGS

  • Kim, Kyung Ho (Department of Mathematics, Korea National University of Transportation)
  • Received : 2019.12.13
  • Accepted : 2020.05.19
  • Published : 2020.08.15
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we extend the notion of a generalized derivation F associated with derivation d to two generalized derivations F and G associated with the same derivation d, as a new idea, to obtain the commutativity of prime rings under certain conditions.

Keywords

References

  1. A. Ali, D. Kumar and P. Miyan, On generalized derivations and commutativity of prime and semiprime rings, Hacet. J. Math. and Stat., 40 (2011), 367-374.
  2. N. Aydin, A note on generalized derivations of prime rings, International Journal of algebra, 5 (2007), 1481-1486.
  3. H. E. Bell and W. S. Martindale III, Semiderivations and commutatity in prime rings, Canad. Math., 31 (1988), no. 4, 500-5008. https://doi.org/10.4153/CMB-1988-072-9
  4. J. Bergen and P. Grzesczuk, Skew derivations with central invariants, J. London Math. Soc., 59 (1999), no. 2, 87-99. https://doi.org/10.1112/S0024610799007000
  5. M. Bresar and J. Vukman, On some additive mappings in rings with involution, Aequationes Math., 38 (1989), 178-185. https://doi.org/10.1007/BF01840003
  6. M. Bresar and J. Vukman, On left derivations and related mappings, Proc. Amer. Math. Soc., 110 (1990), 7-16. https://doi.org/10.1090/S0002-9939-1990-1028284-3
  7. Chang. J. C., On semiderivations of prime rings, Chinese J. Math Soc., 12 (1984), 255-262.
  8. Firat. A., Some results for semiderivations of prime rings, International J. of pure and Applied Mathematics, 28 (1990), no.3, 363-368.
  9. E. C. Posner, Derivations in prime rings, Proc. Amer. Math. Soc., 8 (1957), 1093-1100. https://doi.org/10.1090/S0002-9939-1957-0095863-0
  10. A. Shakir and A. Fosner, On Jordan (α, β)*-derivations in rings, International Journal of Algebra, 1 (2010), no. 4, 99-108.