DOI QR코드

DOI QR Code

On Orthogonal Generalized (σ, τ)-Derivations of Semiprim Near-Rings

Huang, Shuliang

  • Received : 2010.03.19
  • Accepted : 2010.08.27
  • Published : 2010.09.30

Abstract

In this paper, we present some results concerning orthogonal generalized (${\sigma},{\tau}$)-derivations in semiprime near-rings. These results are a generalization of result of Bresar and Vukman, which are related to a theorem of Posner for the product of two derivations in prime rings.

Keywords

Semiprime near-ring;orthogonal generalized (${\sigma},{\tau}$)-derivation;${\alpha}$-centralizer

References

  1. M. Ashraf, A. Ali and S. Ali, (${\sigma},\;{\tau}$)-derivations on prime near-rings, Arch. Math., (Brno), 40(2004), 281-286.
  2. N. Argac, A. Nakajima and E. Albas, On orthogonal generalized derivations of semiprime rings, Turk J. Math., 28(2004), 185-194.
  3. H. E. Bell and G. Mason, On derivations in near-rings, Near-rings and Near-fields, 1987, 31-35.
  4. M. Bresar and J. Vukman, Orthogonal derivations and an extension of a theorem of Posner, Rad. Math., 5(1989), 237-246.
  5. K. I. Beidar, Y. Fong, W. F. Ke and S. Y. Liang, Near-ring multiplication on groups, Comm. Algebra, 23(1995), 999-1015. https://doi.org/10.1080/00927879508825264
  6. J. R. Clay, Nearrings geneses and applications, Oxford University Press, New York, 1992.
  7. O. Golbasi and N. Aydin, Orthogonal generalized (${\sigma},\;{\tau}$)-derivations of semiprime rings, Siberian Mathematical Journal, 48(2007), 979-983. https://doi.org/10.1007/s11202-007-0100-7
  8. K. H. Park and Y. S. Jung, Semiprime near-rings with orthogonal derivations, J. Korea Soc. Math. Edu. Ser.B: Pure Appl. Math., 13(2006), 303-310.
  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