International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 39, Pages 2097-2102

A note on a pair of derivations of semiprime rings

Muhammad Anwar Chaudhry and A. B. Thaheem

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

Received 17 February 2003

Copyright © 2004 Muhammad Anwar Chaudhry and A. B. Thaheem. 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 study certain properties of derivations on semiprime rings. The main purpose is to prove the following result: let R be a semiprime ring with center Z(R), and let f, g be derivations of R such that f(x)x+xg(x)Z(R) for all xR, then f and g are central. As an application, we show that noncommutative semisimple Banach algebras do not admit nonzero linear derivations satisfying the above central property. We also show that every skew-centralizing derivation f of a semiprime ring R is skew-commuting.