Identities with Engel conditions on derivations
Journal
Monatshefte fur Mathematik
Journal Volume
165
Journal Issue
3-4
Pages
543-556
Date Issued
2012
Author(s)
Abstract
Let R be a semiprime ring with a derivation D. The focus is on the two identities with Engel condition on D:[x m, D(x n1),...,D(x ns)] s=0 for all x∈R and D:[x m, D(x) n1,...,D(x) ns] s=0 for all x∈where s, m, n 1,..., n s are fixed positive integers. Our results are natural generalizations of Posner's theorem on centralizing derivations, Herstein's theorem on derivations with power-central values and a recent result by A. Fošner, M. Fošner and Vukman. © 2010 Springer-Verlag.
Type
journal article