International Journal of Mathematics and Mathematical Sciences 
Volume 20 (1997), Issue 2, Pages 413-415
doi:10.1155/S0161171297000562

A note on semiprime rings with derivation

Motoshi Hongan

 Tsuyama College of Technology Numa, Tsuyama, Okayama 708, Japan
Received 26 September 1995; Revised 3 March 1996

Dedicated to the memory of Professor H. Tominaga

Abstract

Let R be a 2-torsion free semiprime ring, I a nonzero ideal of R, Z the center of R and D:R→R a derivation. If d[x,y]+[x,y]∈Z or d[x,y]−[x,y]∈Z for all x, y∈I, then R is commutative.