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International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 6, Pages 917-923
http://dx.doi.org/10.1155/IJMMS.2005.917

On strong commutativity-preserving maps

Department of Mathematical Sciences, College of Scinces, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia

Received 4 July 2004; Revised 4 December 2004

Copyright © 2005 Hindawi Publishing Corporation. 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

We identify some strong commutativity-preserving maps on semiprime rings. Among other results, we prove the following. (i) A centralizing homomorphism f of a semiprime ring R onto itself is strong commutativity preserving. (ii) A centralizing antihomomorphism f of a 2-torsion-free semiprime ring R onto itself is strong commutativity preserving.