DOI QR코드

DOI QR Code

SOME COMMUTATIVITY THEOREMS OF PRIME RINGS WITH GENERALIZED (σ, τ)-DERIVATION

  • Golbasi, Oznur (Department of Mathematics Faculty of Science Cumhuriyet University) ;
  • Koc, Emine (Department of Mathematics Faculty of Science Cumhuriyet University)
  • Received : 2010.04.07
  • Published : 2011.07.31

Abstract

In this paper, we extend some well known results concerning generalized derivations of prime rings to a generalized (${\sigma}$, ${\tau}$)-derivation.

Keywords

References

  1. N. Argac, A. Kaya, and A. Kisir, (${\sigma}$, ${\tau}$)-derivations in prime rings, Math. J. Okayama Univ. 29 (1987), 173-177.
  2. M. Ashraf, A. Asma, and R. Rekha, On generalized derivations of prime rings, Southeast Asian Bull. Math. 29 (2005), no. 4, 669-675.
  3. M. Ashraf, A. Asma, and A. Shakir, Some commutativity theorems for rings with generalized derivations, Southeast Asian Bull. Math. 31 (2007), no. 3, 415-421.
  4. N. Aydin and K. Kaya, Some generalizations in prime rings with (${\sigma}$, ${\tau}$)-derivation, Doga Mat. 16 (1992), no. 3, 169-176.
  5. H. E. Bell and M. N. Daif, On commutativity and strong commutativity-preserving maps, Canad. Math. Bull. 37 (1994), no. 4, 443-447. https://doi.org/10.4153/CMB-1994-064-x
  6. H. E. Bell and W. S. Martindale, Centralizing mappings of semiprime rings, Canad. Math. Bull. 30 (1987), no. 1, 92-101. https://doi.org/10.4153/CMB-1987-014-x
  7. M. Bresar, On the distance of the composition of two derivations to the generalized derivations, Glasgow Math. J. 33 (1991), no. 1, 89-93. https://doi.org/10.1017/S0017089500008077
  8. M. Bresar, Commuting traces of biadditive mappings, commutativity-preserving mappings and Lie mappings, Trans. Amer. Math. Soc. 335 (1993), no. 2, 525-546. https://doi.org/10.2307/2154392
  9. J. C. Chang, On (${\alpha}$, ${\beta}$)-derivations of prime rings, Chinese Journal Math. 22 (1991), no. 1, 21-30.
  10. M. N. Daif and H. E. Bell, Remarks on derivations on semiprime rings, Internat. J. Math. Math. Sci. 15 (1992), no. 1, 205-206. https://doi.org/10.1155/S0161171292000255
  11. Q. Deng and M. Ashraf, On strong commutativity preserving mappings, Results Math. 30 (1996), no. 3-4, 259-263. https://doi.org/10.1007/BF03322194

Cited by

  1. A Note on the Commutativity of Prime Near-rings vol.22, pp.03, 2015, https://doi.org/10.1142/S1005386715000310
  2. On Generalized ()-Derivations in Semiprime Rings vol.2012, 2012, https://doi.org/10.5402/2012/120251