International Journal of Mathematics and Mathematical Sciences
Volume 2009 (2009), Article ID 696737, 6 pages
doi:10.1155/2009/696737
Dependent elements of derivations on semiprime rings.
Faisal Ali
and Muhammad Anwar Chaudhry
Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan, Pakistan
Abstract
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 U⊕V is an essential ideal of R, U∩V={0}, d=0 on U, d(V)⊆V, and d acts freely on V.