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 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
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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 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 -