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

Cheng-Kai Liu

doi:10.1016/j.laa.2014.06.003

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

Cheng-Kai Liu

Department of Mathematics

Research output: Contribution to journal › Article

16 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,y^GLn(D). The analogous result for singular matrices is also obtained.

Original language	English
Pages (from-to)	280-290
Number of pages	11
Journal	Linear Algebra and Its Applications
Volume	458
DOIs	https://doi.org/10.1016/j.laa.2014.06.003
Publication status	Published - 2014 Oct 1

All Science Journal Classification (ASJC) codes

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

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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, 458, 280-290. https://doi.org/10.1016/j.laa.2014.06.003

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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.",

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AB - 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.

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