Remarks on Derivations on Semiprime Rings

Abstract

We prove that a semiprime ring R must be commutative if it admits a derivation d such that (i) xy + d(xy) = yx + d(yx) for all x,y in R, or (ii) xy – d(xy)~ yx – d(yx) for all x,y in R. In the event that R is prime, (i) or (ii) need only be assumed for all x,y in some nonzero ideal of R. © 1992, Hindawi Publishing Corporation. All rights reserved.