DOI QR코드

DOI QR Code

ON (σ, τ)-LIE IDEALS WITH GENERALIZED DERIVATION

  • Golbasi, Oznur (DEPARTMENTS OF MATHEMATICS FACULTY OF ARTS AND SCIENCE CUMHURIYET UNIVERSITY) ;
  • Koc, Emine (DEPARTMENTS OF MATHEMATICS FACULTY OF ARTS AND SCIENCE CUMHURIYET UNIVERSITY)
  • Received : 2008.12.16
  • Published : 2010.11.30

Abstract

In the present paper, we extend some well known results concerning derivations of prime rings to generalized derivations for ($\sigma,\tau$)-Lie ideals.

Keywords

References

  1. E. Albas and N. Argac, Generalized derivations of prime rings, Algebra Colloq. 11 (2004), no. 3, 399-410.
  2. N. Argac, On prime and semiprime rings with derivations, Algebra Colloq. 13 (2006), no. 3, 371-380. https://doi.org/10.1142/S1005386706000320
  3. N. Aydin, On one sided $({\sigma},{\tau}-Lie$ ideals in prime rings, Turkish J. Math. 21 (1997), no. 3, 295-301.
  4. N. Aydin and H. Kandamar, $({\sigma},{\tau}-Lie$ ideals in prime rings, Turkish J. Math. 18 (1994), no. 2, 143-148.
  5. N. Aydin, K. Kaya, and O. Golbasi, Some results on one-sided generalized Lie ideals with derivation, Math. Notes (Miskolc) 3 (2002), no. 2, 83-89.
  6. N. Aydin and M. Soyturk, $({\sigma},{\tau})-Lie$ ideals in prime rings with derivation, Turkish J. Math. 19 (1995), no. 3, 239-244.
  7. J. Bergen, I. N. Herstein, and J. W. Kerr, Lie ideals and derivations of prime rings, J. Algebra 71 (1981), no. 1, 259-267. https://doi.org/10.1016/0021-8693(81)90120-4
  8. 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
  9. 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
  10. O. Golbasi and K. Kaya, On Lie ideals with generalized derivations, Sibirsk. Mat. Zh. 47 (2006), no. 5, 1052-1057; translation in Siberian Math. J. 47 (2006), no. 5, 862-866.
  11. I. N. Herstein, On the Lie structure of an associative ring, J. Algebra 14 (1970), 561-571. https://doi.org/10.1016/0021-8693(70)90103-1
  12. I. N. Herstein, A note on derivations, Canad. Math. Bull. 21 (1978), no. 3, 369-370. https://doi.org/10.4153/CMB-1978-065-x
  13. I. N. Herstein, A note on derivations. II, Canad. Math. Bull. 22 (1979), no. 4, 509-511. https://doi.org/10.4153/CMB-1979-066-2
  14. B. Hvala, Generalized derivations in rings, Comm. Algebra 26 (1998), no. 4, 1147-1166. https://doi.org/10.1080/00927879808826190
  15. K. Kaya, $({\sigma,{\tau})-Lie$ ideals in prime rings, An. Univ. Timisoara Ser. Stiinte Math. 30 (1992), no. 2-3, 251-255.
  16. K. Kaya and N. Aydin, Some results in generalized Lie ideals, Albasapr Sci. J. Isued by Jordan University for Woman 3 (1999), no. 1, 53-61.
  17. 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