Commutators with power central values on a Lie ideal

Luisa Carini and Vincenzo De Filippis

Vol. 193 (2000), No. 2, 269–278

DOI: 10.2140/pjm.2000.193.269

Abstract

Let R be a prime ring of characteristic ≠2 with a derivation d≠0, L a noncentral Lie ideal of R such that [d(u),u]ⁿ is central, for all u ∈ L. We prove that R must satisfy s₄ the standard identity in 4 variables. We also examine the case R is a 2-torsion free semiprime ring and [d([x,y]),[x,y]]ⁿ is central, for all x,y ∈ R.

Milestones

Received: 19 August 1998

Revised: 20 November 1998

Published: 1 April 2000