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International Journal of Mathematics and Mathematical Sciences
Volume 2014 (2014), Article ID 216039, 8 pages
http://dx.doi.org/10.1155/2014/216039
Research Article

Generalized Derivations on Power Values of Lie Ideals in Prime and Semiprime Rings

1Department of Mathematics and Computer Science, University of Messina, Viale Ferdinando Stagno d’Alcontres 31, 98166 Messina, Italy
2Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
3Faculty of Science, Islamic University in Madinah, P.O. Box 170, Madinah 42351, Saudi Arabia

Received 3 January 2014; Accepted 12 May 2014; Published 3 June 2014

Academic Editor: Kaiming Zhao

Copyright © 2014 Vincenzo De Filippis et al. 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.

Abstract

Let be a 2-torsion free ring and let be a noncentral Lie ideal of , and let and be two generalized derivations of . We will analyse the structure of in the following cases: (a) is prime and for all and fixed positive integers ; (b) is prime and for all and fixed integers ; (c) is semiprime and for all and fixed integer ; and (d) is semiprime and for all and fixed integer .