A result on generalized derivations on right ideals of prime rings


Let R be a prime ring of characteristic other than 2 and let I be a nonzero right ideal of R. Also let U be the right Utumi quotient ring of R and let C be the center of U. If G is a generalized derivation of R such that [[G(x), x], G(x)] = 0 for all x ? I, then R is commutative or there exist a, b ? U such that G(x) = ax + xb for all x ? R and one of the following assertions is true:(1) (a - ?)I = (0) = (b + ?)I for some ? ? C,(2) (a - ?)I = (0) for some ? ? C and b ? C. © 2012 Springer Science+Business Media, Inc

Similar works

This paper was published in Ege University Institutional Repository.

Having an issue?

Is data on this page outdated, violates copyrights or anything else? Report the problem now and we will take corresponding actions after reviewing your request.