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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.

Abstract

Let be a semiprime ring, a nonzero ideal of , and , two epimorphisms of . An additive mapping is generalized -derivation on if there exists a -derivation such that holds for all . In this paper, it is shown that if , then contains a nonzero central ideal of , if one of the following holds: (i) ; (ii) ; (iii) ; (iv) ; (v) for all .