Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan, Pakistan
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 on a semiprime ring and investigate a decomposition of using dependent elements of . We show that there exist ideals and of such that is an essential ideal of , , on , , and acts freely on .