10.1007/s11253-012-0637-x

A result on generalized derivations on right ideals of prime rings

Abstract

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

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This paper was published in Ege University Institutional Repository.

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