Table of Contents
ISRN Algebra
Volume 2014, Article ID 684792, 8 pages
http://dx.doi.org/10.1155/2014/684792
Research Article

On Generalized Jordan Triple -Higher Derivations in Prime Rings

Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India

Received 25 October 2013; Accepted 26 November 2013; Published 22 January 2014

Academic Editors: V. De Filippis, T. Nakatsu, and U. Vishne

Copyright © 2014 Mohammad Ashraf and Almas Khan. 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 and let be a Lie ideal of . Suppose that are endomorphisms of , and is the set of all nonnegative integers. A family of mappings is said to be a generalized -higher derivation (resp., generalized Jordan triple -higher derivation) of if there exists a -higher derivation of such that , the identity map on , , and (resp., hold for all and for every If the above conditions hold for all , then is said to be a generalized -higher derivation (resp., generalized Jordan triple -higher derivation) of into . In the present paper it is shown that if is a noncentral square closed Lie ideal of a prime ring of characteristic different from two, then every generalized Jordan triple -higher derivation of into is a generalized -higher derivation of into .