International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 3, Pages 471-474
doi:10.1155/S0161171298000660
Commutativity results for semiprime rings with derivations
Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City, Cairo 11884, Egypt
Received 8 March 1996; Revised 10 October 1996
Copyright © 1998 Mohammad Nagy Daif. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.