DOI QR코드

DOI QR Code

ON SYMMETRIC GENERALIZED 3-DERIVATIONS AND COMMUTATIVITY IN PRIME NEAR-RINGS

  • Received : 2009.03.09
  • Accepted : 2009.06.02
  • Published : 2009.06.25

Abstract

In this note, we introduce a symmetric generalized 3-derivation in near-rings and investigate some conditions for a nearring to be a commutative ring.

Keywords

References

  1. M. Ashraf, A. Ali and S. Ali, $({\sigma},{\tau})$-derivations on prime near-rings, Archivum Mathematicum (BRNO), Tomus. 40 (2004), 281-286.
  2. H.E. Bell, On prime near-rings with generalized derivation, Internat. J. Math. & Math. Sci. 2008 (2008), 1-5.
  3. H.E. Bell and G. Mason, On derivations in near-rings, in Near-Rings and Near-Fields (Tubingen, 1985), G. Betsch, Ed., vol, 137 of North-Holland Mathematics Studies, pp. 31-35, North-Holland, Amsterdam, The Netherlands, 1987.
  4. M. Bresar, On the distance of the compositions of two derivations to the generalized derivations, Glasgow Math. J. 33 (1991), 89-93. https://doi.org/10.1017/S0017089500008077
  5. M. Bresar, Commuting mops: a survey, Taiwanese J. Math. 8(3) (2004), 361-397. https://doi.org/10.11650/twjm/1500407660
  6. Y. Ceven and M.A. Ozturk, Some properties of symmetric bi-$({\sigma},{\tau})$-derivations in near-rings, Commun. Korean Math. Soc. 22(4) (2007), 487-491. https://doi.org/10.4134/CKMS.2007.22.4.487
  7. O. Golbasi, On prime near-rings with generalized $({\sigma},{\tau})$-derivations, Kyungpook Mach. J. 45 (2005), 249-254.
  8. O. Golbasi, Notes on prime near-rings with generalized derivation, Southeast Asian Bull. Math. 30(1) (2006), 49-54.
  9. B. Hvala, Generalized derivations in prime rings, Comm. Aigebra., 26(4) (1998), 1147-1166. https://doi.org/10.1080/00927879808826190
  10. G. Pilz, Near-rings, 2nd Ed. North Holland, Amsterdam, 1983.
  11. 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
  12. M.A. Quadri, M.S. Khan and N. Rehman, Generalized derivations and commutativity of prime rings, Indian J. pure appl. Math. 34(9) (2003), 1393-1396.
  13. P. Ribenboim, Higher order derivations of modules, Portgaliae Math. 39 (1980), 381-397.
  14. M. Uckun and M.A. Ozturk, On trace of symmetric bi-gamma-derivations in gamma-near-rings, Houston J. Math. 33(2) (2007), 323-339.
  15. J. Vukman, Symmetric bi-derivations on prime and semi-prime rings, Aequationes Math. 38 (1989), 245-254. https://doi.org/10.1007/BF01840009
  16. J. Vukman, Two results concerning symmetric bi-derivations on prime rings, Aequationes Math. 40 (1990), 181-189. https://doi.org/10.1007/BF02112294