A note on semiprime rings with derivation

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.

Keywords

• derivation
• semiprime ring
• 2-torsion free ring.