International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 6, Pages 917-923
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 M. S. Samman. 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.
We identify some strong commutativity-preserving maps on
semiprime rings. Among other results, we prove the following.
(i) A centralizing homomorphism of a semiprime ring onto itself is strong commutativity preserving. (ii) A
centralizing antihomomorphism of a 2-torsion-free
semiprime ring onto itself is strong