On Certain Subgroups of Semiprime Rings with Derivations

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] ∣ x ∈ I} contains a noncentral Lie ideal of R.

Key Words:

• Derivation
• Lie ideal
• Prime ring
• Semiprime ring
• Maximal right quotient ring
• Orthogonal completions

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.