International Journal of Mathematics and Mathematical Sciences
Volume 20 (1997), Issue 2, Pages 263-266
On a conjecture of Vukman
Department of Mathematics, Southwest China Normal University, Chongqing 630715, China
Received 27 October 1993; Revised 30 October 1995
Copyright © 1997 Qing Deng. 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.
Let be a ring bi-additive symmetric mapping is called a symmetric
bi-derivation if, for any fixed , the mapping is a derivation. The purpose of this paper
is to prove the following conjecture of Vukman.
Let be a noncommutative prime ring with suitable characteristic restrictions, and let
and be a symmetric bi-derivation and its trace, respectively. Suppose
that for all , where for and , then .