Semi-centralizing maps of generalized matrix algebras
type: Item
instance of: scholarly article
title: Semi-centralizing maps of generalized matrix algebras
zbMATH Open document ID: 1238.15015
author: Yanbo Li
author: Feng Wei
published in: Linear Algebra and its Applications
publication date: 2012-03-07T00:00:00Z
review text: The present article is a continuation of a former work by \textit{Z. Xiao} and \textit{F. Wei} [Linear Algebra Appl. 433, No. 11--12, 2178--2197 (2010; Zbl 1206.15016)]. Motivated by Brešar's and Cheung's ideas, the authors study semi-centralizing maps of generalized matrix algebras and describe its general form by routine and complicated computations. Skew-commuting maps and semi-centralizing maps of generalized matrix algebras are specially considered. They prove that any skew-commuting map on a class of generalized matrix algebras is zero and that any semi-centralizing derivation on a generalized matrix algebra is zero. These results give new perspectives to the work of \textit{M. Brešar} [Taiwanese J. Math. 8, No. 3, 361--397 (2004; Zbl 1078.16032)] and extend the main results of \textit{W.-S. Cheung} [J. Lond. Math. Soc., II. Ser. 63, No. 1, 117--127 (2001; Zbl 1014.16035)]. A number of applications related to semi-centralizing maps are given.
Mathematics Subject Classification ID: 15A78
Mathematics Subject Classification ID: 16W25
Mathematics Subject Classification ID: 47L35
Mathematics Subject Classification ID: 15A30
zbMATH DE Number: 6012747
zbMATH Keywords: generalized matrix algebra
zbMATH Keywords: semi-centralizing map
zbMATH Keywords: skew-commuting map
zbMATH Keywords: semi-centralizing derivation
reviewed by: Andreas Arvanitoyeorgos
MaRDI profile type: Publication
full work available at URL: j.laa.2011.07.014
OpenAlex ID: W1981374811
cites work: Lie derivations on triangular matrices
cites work: Commuting traces and commutativity preserving maps on triangular algebras.
cites work: Commuting Traces of Biadditive Mappings, Commutativity-Preserving Mappings and Lie Mappings
cites work: On skew-commuting mappings of rings
cites work: Centralizing mappings and derivations in prime rings
cites work: Commuting maps: a survey.
cites work: Jordan derivations revisited
cites work: The range and kernel inclusion of algebraic derivations and commuting maps
cites work: Q3417002
cites work: Generalized Matrix Algebras
cites work: Lie Derivations of Triangular Algebras
cites work: Commuting Maps of Triangular Algebras
cites work: On Semicommuting Automorphisms of Rings
cites work: Q3994569
cites work: Q3832703
cites work: On codimension growth of finitely generated associative algebras
cites work: Minimal varieties of algebras of exponential growth.
cites work: Jordan \((\alpha,\beta)\)-derivations on triangular algebras and related mappings.
cites work: Q3043336
cites work: Symmetric amenability and the nonexistence of Lie and Jordan derivations
cites work: Triangular Operator Algebras: Fundamentals and Hyperreducible Theory
cites work: A characteristic free approach to Brauer algebras
cites work: Isomorphism of generalized matrix rings
cites work: Commutativity preserving linear maps and Lie automorphisms of triangular matrix algebras
cites work: Centralizing Automorphisms of Prime Rings
cites work: Q3495525
cites work: Derivations in Prime Rings
cites work: Additive Lie (\(\xi \)-Lie) derivations and generalized Lie (\(\xi \)-Lie) derivations on nest algebras
cites work: Radicals and Morita contexts
cites work: PAIRS OF DERIVATIONS ON RINGS AND BANACH ALGEBRAS
cites work: Jordan higher derivations on triangular algebras
cites work: Commuting mappings of generalized matrix algebras
cites work: Q5456143
cites work: Nonlinear Lie derivations of triangular algebras.
DOI: 10.1016/J.LAA.2011.07.014
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description: scientific article; zbMATH DE number 6012747