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

Cheng-Kai Liu

Research output: Contribution to journal › Article

15 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

Liu, Cheng-Kai. / Strong commutativity preserving maps on subsets of matrices that are not closed under addition. In: Linear Algebra and Its Applications. 2014 ; Vol. 458. pp. 280-290.
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Liu, C-K 2014, 'Strong commutativity preserving maps on subsets of matrices that are not closed under addition', Linear Algebra and Its Applications, vol. 458, pp. 280-290. https://doi.org/10.1016/j.laa.2014.06.003

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 journal › Article

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Liu C-K. Strong commutativity preserving maps on subsets of matrices that are not closed under addition. Linear Algebra and Its Applications. 2014 Oct 1;458:280-290. https://doi.org/10.1016/j.laa.2014.06.003

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