International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 6, Pages 917-923
doi:10.1155/IJMMS.2005.917
On strong commutativity-preserving maps.
M.S. Samman
Department of Mathematical Sciences, College of Scinces, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
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.