Power-Centralizing Automorphisms of Lie Ideals in Prime Rings

ABSTRACT

Let R be a prime ring with center Z, L a noncentral Lie ideal of R, and σ a nontrivial automorphism of R such that [u ^σ,u] ⁿ  ∈ Z for all u ∈ L. If either char(R) > n or char(R) = 0, then R satisfies s ₄, the standard identity in 4 variables.

Keywords:

• Automorphism
• Lie ideal
• Prime ring

Mathematics Subject Classification:

• 16N60
• 16W20

ACKNOWLEDGMENT

The author is deeply thankful to both Professor Fenwen Niu for his helpful suggestions and the referee for his careful reading of the paper.

Notes

Communicated by M. Bresar.