Table of Contents
ISRN Algebra
Volume 2013, Article ID 738368, 7 pages
http://dx.doi.org/10.1155/2013/738368
Research Article

Semiderivations Satisfying Certain Algebraic Identities on Jordan Ideals

1Department of Mathematics and Computer Science, University of Messina, 98166 Messina, Italy
2Université Moulay Ismail, Faculté des Sciences et Techniques, Département de Mathématiques, BP 509, Boutalamine, 52000 Errachidia, Morocco

Received 7 April 2013; Accepted 27 May 2013

Academic Editors: V. Drensky, K. Fujii, M. Ladra, J. van de Leur, A. Woldar, S. Yang, and Y. Zhou

Copyright © 2013 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 ring. An additive mapping is called semiderivation of if there exists an endomorphism of such that and , for all in . Here we prove that if is a 2-torsion free -prime ring and a nonzero -Jordan ideal of such that for all , then either is commutative or for all . Moreover, we initiate the study of generalized semiderivations in prime rings.