Abstract

We extend a result of Herstein concerning a derivation d on a prime ring R satisfying [d(x),d(y)]=0 for all x,y∈R, to the case of semiprime rings. An extension of this result is proved for a two-sided ideal but is shown to be not true for a one-sided ideal. Some of our recent results dealing with U*- and U**- derivations on a prime ring are extended to semiprime rings. Finally, we obtain a result on semiprime rings for which d(xy)=d(yx) for all x,y in some ideal U.