### 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 |
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Pages (from-to) | 280-290 |

Number of pages | 11 |

Journal | Linear Algebra and Its Applications |

Volume | 458 |

DOIs | |

Publication status | Published - 2014 Oct 1 |

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

Research output: Contribution to journal › Article

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 -