Dependent Elements of Derivations on Semiprime Rings - Faisal Ali; Muhammad Anwar Chaudhry (International Journal of Mathematics and Mathematical Sciences)
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.