Abstract
Let R be a 2-torsion free semiprime ring, and let I be a dense ideal of R. Suppose that d is a derivation from I to R such that I d does not lie in the center of R. Then the additive subgroup of R generated by {[x d , x]āā£āxāāāI} contains a noncentral Lie ideal of R.
Acknowledgments
The author would like to express her sincere thanks to the referee for useful suggestions and comments and to Professors M.A. Chebotar, W.-F. Ke and T.-K. Lee for valuable discussions and their help in writing this paper. Research supported by NSC Grants NSC90-2115-M-110-010.
Notes
#Communicated by M. Ferrero.