Table of Contents
ISRN Algebra
Volume 2012, Article ID 302524, 6 pages
http://dx.doi.org/10.5402/2012/302524
Research Article

Powers of Commutators and Anticommutators

1Department of Mathematics and Statistics, National University of Ireland Maynooth, Maynooth, Kildare, Ireland
2School of Mathematical Sciences, University College Cork, Cork, Ireland

Received 14 November 2012; Accepted 5 December 2012

Academic Editors: D. Anderson, A. V. Kelarev, A. Kiliçman, D. Sage, and A. Zimmermann

Copyright © 2012 Stephen M. Buckley and Desmond MacHale. 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

For , we give elementary proofs of commutativity of rings in which the identity holds for all commutators . For even , we show that the commutativity of rings satisfying such an identity is equivalent to the anticommutativity of rings satisfying the corresponding anticommutator equation.