Table of Contents
International Scholarly Research Notices
Volume 2014 (2014), Article ID 563284, 9 pages
http://dx.doi.org/10.1155/2014/563284
Research Article

Two-Sided Annihilator Condition with Generalized Derivations on Multilinear Polynomials

Department of Mathematics, Faculty of Sciences, University of Messina, Via F. Stagno D’Alcontres 31, 98166 Messina, Italy

Received 30 April 2014; Accepted 15 July 2014; Published 28 October 2014

Academic Editor: Ali Jaballah

Copyright © 2014 V. 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 prime ring of characteristic different from 2, with extended centroid , its two-sided Utumi quotient ring, a nonzero generalized derivation of , a noncentral multilinear polynomial over in noncommuting variables, and such that for any . Then one of the following holds: (1) ; (2) ; (3) there exists such that , for all ; (4) there exist and such that , for all , and is central valued on ; (5) there exist and such that , for all , and , .