ON CERTAIN SUBGROUPS OF PRIME RINGS WITH DERIVATIONS

Abstract

Let R be a noncommutative prime ring and let d be a nonzero derivation on R. A classical theorem of Posner asserts that the subset {[x ^d , x]|x ∈ R} is not contained in the center of R. Under the additional assumption that char R ≠ 2 and d ³ ≠ 0, we show that the additive subgroup of R generated by the subset {[x ^d , x] | x ∈ R} contains a noncentral Lie ideal of R.

Acknowledgments