On Lie Automorphisms, Additive Subgroups, and Lie Ideals of Prime Rings

Abstract

Let R be a prime ring of characteristic not equal to 2 or 3 and let L be a noncentral Lie ideal of R. Suppose that σ is a Lie automorphism on L such that σ⁴ is not the identity map. Then the additive subgroup generated by the set {[x ^σ, x] ∣ x ∈ L} contains a noncentral Lie ideal of R.

Key Words:

• Prime ring
• Lie automorphism
• Lie ideal
• Generalized polynomial identity

Acknowledgment

The author would like to express her sincere thanks to professors Chebotar and Ke for valuable discussions and their help in writing this paper.