Strong commutativity preserving maps on subsets of matrices that are not closed under addition

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

Let Mn(D) be the ring of all n×n matrices over a division ring D, where n≥2 is an integer and let GLn(D) be the set of all invertible matrices in Mn(D). We describe maps f:GLn(D) →Mn(D) such that [f(x),f(y)]=[x,y] for all x,yGLn(D). The analogous result for singular matrices is also obtained.

Original languageEnglish
Pages (from-to)280-290
Number of pages11
JournalLinear Algebra and Its Applications
Volume458
DOIs
Publication statusPublished - 2014 Oct 1

Fingerprint

Invertible matrix
Singular matrix
Division ring or skew field
Commutativity
Ring
Closed
Integer
Subset

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

Cite this

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title = "Strong commutativity preserving maps on subsets of matrices that are not closed under addition",
abstract = "Let Mn(D) be the ring of all n×n matrices over a division ring D, where n≥2 is an integer and let GLn(D) be the set of all invertible matrices in Mn(D). We describe maps f:GLn(D) →Mn(D) such that [f(x),f(y)]=[x,y] for all x,yGLn(D). The analogous result for singular matrices is also obtained.",
author = "Cheng-Kai Liu",
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journal = "Linear Algebra and Its Applications",
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publisher = "Elsevier Inc.",

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Strong commutativity preserving maps on subsets of matrices that are not closed under addition. / Liu, Cheng-Kai.

In: Linear Algebra and Its Applications, Vol. 458, 01.10.2014, p. 280-290.

Research output: Contribution to journalArticle

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