Table of Contents
Algebra
Volume 2014 (2014), Article ID 672387, 9 pages
http://dx.doi.org/10.1155/2014/672387
Research Article

Jordan Higher Derivable Mappings on Rings

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

Received 15 August 2014; Accepted 29 October 2014; Published 19 November 2014

Academic Editor: Hong You

Copyright © 2014 Mohammad Ashraf and Nazia Parveen. 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. We say that a family of maps is a Jordan higher derivable map (without assumption of additivity) on if (the identity map on ) and hold for all and for each . In this paper, we show that every Jordan higher derivable map on a ring under certain assumptions becomes a higher derivation. As its application, we get that every Jordan higher derivable map on Banach algebra is an additive higher derivation.