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.