International Journal of Mathematics and Mathematical Sciences
Volume 2009 (2009), Article ID 696737, 6 pages
Research Article

Dependent Elements of Derivations on Semiprime Rings

Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan, Pakistan

Received 15 October 2008; Accepted 19 February 2009

Academic Editor: Nils-Peter Skoruppa

Copyright © 2009 Faisal Ali and Muhammad Anwar Chaudhry. 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 characterize dependent elements of a commuting derivation d on a semiprime ring R and investigate a decomposition of R using dependent elements of d. We show that there exist ideals U and V of R such that UV is an essential ideal of R, UV={0}, d=0 on U, d(V)V, and d acts freely on V.