Abstract
Let D be a division ring and let Mn(D) be the ring of all n×n matrices over D with center Z, where n≥2 is an integer. We describe the additive map f: Mn (D)→ Mn (D) such that f(x)x-xf(x)∈Z for all invertible (singular) x∈Mn(D).
| Original language | English |
|---|---|
| Pages (from-to) | 318-324 |
| Number of pages | 7 |
| Journal | Linear Algebra and Its Applications |
| Volume | 440 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2014 Jan 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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Centralizing maps on invertible or singular matrices over division rings. / Liu, Cheng-Kai.
In: Linear Algebra and Its Applications, Vol. 440, No. 1, 01.01.2014, p. 318-324.Research output: Contribution to journal › Article
TY - JOUR
T1 - Centralizing maps on invertible or singular matrices over division rings
AU - Liu, Cheng-Kai
PY - 2014/1/1
Y1 - 2014/1/1
N2 - Let D be a division ring and let Mn(D) be the ring of all n×n matrices over D with center Z, where n≥2 is an integer. We describe the additive map f: Mn (D)→ Mn (D) such that f(x)x-xf(x)∈Z for all invertible (singular) x∈Mn(D).
AB - Let D be a division ring and let Mn(D) be the ring of all n×n matrices over D with center Z, where n≥2 is an integer. We describe the additive map f: Mn (D)→ Mn (D) such that f(x)x-xf(x)∈Z for all invertible (singular) x∈Mn(D).
UR - http://www.scopus.com/inward/record.url?scp=84889878390&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84889878390&partnerID=8YFLogxK
U2 - 10.1016/j.laa.2013.10.016
DO - 10.1016/j.laa.2013.10.016
M3 - Article
AN - SCOPUS:84889878390
VL - 440
SP - 318
EP - 324
JO - Linear Algebra and Its Applications
JF - Linear Algebra and Its Applications
SN - 0024-3795
IS - 1
ER -