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ISRN Algebra
Volume 2012 (2012), Article ID 120251, 7 pages
http://dx.doi.org/10.5402/2012/120251
Research Article

On Generalized ( )-Derivations in Semiprime Rings

Department of Mathematics, Belda College, Paschim Medinipur, Belda 721424, India

Received 18 October 2012; Accepted 6 November 2012

Academic Editors: A. Jaballah, C. Munuera, and H. You

Copyright © 2012 Basudeb Dhara and Atanu Pattanayak. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. M. Ashraf, N. Rehman, S. Ali, and M. R. Mozumder, “On semiprime rings with generalized derivations,” Boletim da Sociedade Paranaense de Matemática. 3rd Série, vol. 28, no. 2, pp. 25–32, 2010. View at Publisher · View at Google Scholar
  2. M. Ashraf, A. Ali, and S. Ali, “Some commutativity theorems for rings with generalized derivations,” Southeast Asian Bulletin of Mathematics, vol. 31, no. 3, pp. 415–421, 2007.
  3. H. E. Bell and N.-U. Rehman, “Generalized derivations with commutativity and anti-commutativity conditions,” Mathematical Journal of Okayama University, vol. 49, pp. 139–147, 2007.
  4. Q. Deng and H. E. Bell, “On derivations and commutativity in semiprime rings,” Communications in Algebra, vol. 23, no. 10, pp. 3705–3713, 1995. View at Publisher · View at Google Scholar
  5. B. Dhara, “Remarks on generalized derivations in prime and semiprime rings,” International Journal of Mathematics and Mathematical Sciences, vol. 2010, Article ID 646587, 6 pages, 2010. View at Publisher · View at Google Scholar
  6. B. Hvala, “Generalized derivations in rings,” Communications in Algebra, vol. 26, no. 4, pp. 1147–1166, 1998. View at Publisher · View at Google Scholar
  7. E. C. Posner, “Derivations in prime rings,” Proceedings of the American Mathematical Society, vol. 8, pp. 1093–1100, 1957.
  8. M. A. Quadri, M. S. Khan, and N. Rehman, “Generalized derivations and commutativity of prime rings,” Indian Journal of Pure and Applied Mathematics, vol. 34, no. 9, pp. 1393–1396, 2003.
  9. F. Ali and M. A. Chaudhry, “On generalized (α,β)-derivations of semiprime rings,” Turkish Journal of Mathematics, vol. 35, no. 3, pp. 399–404, 2011.
  10. N. Argaç and E. Albas, “On generalized (σ,τ)-derivations,” Sibirskiĭ Matematicheskiĭ Zhurnal, vol. 43, no. 6, pp. 977–984, 2002. View at Publisher · View at Google Scholar
  11. N. Argaç, A. Kaya, and A. Kisir, “(σ,τ)-derivations in prime rings,” Mathematical Journal of Okayama University, vol. 29, pp. 173–177, 1987.
  12. N. Aydın and K. Kaya, “Some generalizations in prime rings with (σ,τ)-derivation,” Turkish Journal of Mathematics, vol. 16, no. 3, pp. 169–176, 1992.
  13. ö. Gölbaşi and E. Koç, “Some commutativity theorems of prime rings with generalized (σ,τ)-derivation,” Communications of the Korean Mathematical Society, vol. 26, no. 3, pp. 445–454, 2011. View at Publisher · View at Google Scholar
  14. E. Gölbaşi and E. Koç, “Notes on generalized (σ,τ)-derivation,” Rendiconti del Seminario Matematico della Università di Padova, vol. 123, pp. 131–139, 2010.
  15. Y.-S. Jung and K.-H. Park, “On generalized (α,β)-derivations and commutativity in prime rings,” Bulletin of the Korean Mathematical Society, vol. 43, no. 1, pp. 101–106, 2006. View at Publisher · View at Google Scholar
  16. H. Marubayashi, M. Ashraf, N. Rehman, and S. Ali, “On generalized (α,β)-derivations in prime rings,” Algebra Colloquium, vol. 17, no. 1, pp. 865–874, 2010.
  17. N. U. Rehman, R. M. AL-Omary, and C. Haetinger, “On Lie structure of prime rings with generalized (α,β)-derivations,” Boletim da Sociedade Paranaense de Matemática, vol. 27, no. 2, pp. 43–52, 2009.
  18. M. N. Daif and H. E. Bell, “Remarks on derivations on semiprime rings,” International Journal of Mathematics and Mathematical Sciences, vol. 15, no. 1, pp. 205–206, 1992. View at Publisher · View at Google Scholar