A note on derivations with power central values on a Lie ideal

Jeffery Marc Bergen and Luisa Carini

Vol. 132 (1988), No. 2, 209–213

DOI: 10.2140/pjm.1988.132.209

Abstract

Let R be a prime ring of characteristic ≠2 with a derivation d≠0 and a non-central Lie ideal U such that d(u)ⁿ is central, for all u ∈ U. We prove that R must satisfy s₄, the standard identity in 4 variables; hence R is either commutative or an order in a 4-dimensional simple algebra. This result extends a theorem of Herstein to Lie ideals.

Mathematical Subject Classification

Primary: 16A72, 16A72

Secondary: 16A70, 16A68

Milestones

Received: 15 January 1987

Published: 1 April 1988