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 › peer-review

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

Access to Document

10.1016/j.laa.2014.06.003

Fingerprint Dive into the research topics of 'Strong commutativity preserving maps on subsets of matrices that are not closed under addition'. Together they form a unique fingerprint.

Cite this

@article{2ad51eb361e5458d84bb55f67364eab4,

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 = "Liu, {Cheng Kai}",

year = "2014",

month = oct,

day = "1",

doi = "10.1016/j.laa.2014.06.003",

language = "English",

volume = "458",

pages = "280--290",

journal = "Linear Algebra and Its Applications",

issn = "0024-3795",

publisher = "Elsevier Inc.",

}

TY - JOUR

T1 - Strong commutativity preserving maps on subsets of matrices that are not closed under addition

AU - Liu, Cheng Kai

PY - 2014/10/1

Y1 - 2014/10/1

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=84903559955&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84903559955&partnerID=8YFLogxK

U2 - 10.1016/j.laa.2014.06.003

DO - 10.1016/j.laa.2014.06.003

M3 - Article

AN - SCOPUS:84903559955

VL - 458

SP - 280

EP - 290

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

ER -