Differential identities, Lie ideals, and Posner’s theorems

Charles Philip Lanski

Vol. 134 (1988), No. 2, 275–297

DOI: 10.2140/pjm.1988.134.275

Abstract

Two well-known results of E. C. Posner state that the composition of two nonzero derivations of a prime ring cannot be a nonzero derivation, and that in a prime ring, if the commutator of each element and its image under a nonzero derivation is central, then the ring is commutative. Our purpose is to show how the theory of differential identities can be used to obtain these results and their generalizations to Lie ideals and to rings with involution.

Mathematical Subject Classification

Primary: 16A72, 16A72

Secondary: 16A68

Milestones

Received: 19 November 1986

Revised: 23 July 1987

Published: 1 October 1988