On maps preserving zeros of Lie polynomials of small degrees
type: Item
instance of: scholarly article
title: On maps preserving zeros of Lie polynomials of small degrees
zbMATH Open document ID: 1185.15025
author: Toan Duc Dinh
author: Michael Donzella
published in: Linear Algebra and its Applications
publication date: 2009-12-18T00:00:00Z
review text: A Lie polynomial is an element of the free algebra generated by some set of variables. In this note, the authors describe maps preserving zeros of multilinear Lie polynomials of degrees \(3\) and \(4\) on prime algebras and matrices over unital algebras. The main techniques are based on functional identities developed by \textit{M. Brešar} [Trans. Am. Math. Soc. 335, No.~2, 525--546 (1993; Zbl 0791.16028) and Isr. J. Math. 162, 317--334 (2007; Zbl 1142.16020)].
Mathematics Subject Classification ID: 15A86
Mathematics Subject Classification ID: 16N60
Mathematics Subject Classification ID: 16R60
zbMATH DE Number: 5649988
zbMATH Keywords: linear preserver problems
zbMATH Keywords: zeros of Lie polynomials
zbMATH Keywords: prime rings
zbMATH Keywords: multilinear Lie polynomials
zbMATH Keywords: prime algebras
zbMATH Keywords: unital algebras
reviewed by: C. M.da Fonseca
MaRDI profile type: Publication
full work available at URL: j.laa.2009.08.026
OpenAlex ID: W1993878897
Wikidata QID: Q115344854
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DOI: 10.1016/J.LAA.2009.08.026
description: scientific article; zbMATH DE number 5649988