Centralizing maps on invertible or singular matrices over division rings

Cheng-Kai Liu

doi:10.1016/j.laa.2013.10.016

Centralizing maps on invertible or singular matrices over division rings

Cheng-Kai Liu

Department of Mathematics

Research output: Contribution to journal › Article

19 Citations (Scopus)

Abstract

Let D be a division ring and let M_n(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: M_n (D)→ M_n (D) such that f(x)x-xf(x)∈Z for all invertible (singular) x∈M_n(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	https://doi.org/10.1016/j.laa.2013.10.016
Publication status	Published - 2014 Jan 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.2013.10.016

Fingerprint Dive into the research topics of 'Centralizing maps on invertible or singular matrices over division rings'. Together they form a unique fingerprint.

Cite this

Liu, C-K. (2014). Centralizing maps on invertible or singular matrices over division rings. Linear Algebra and Its Applications, 440(1), 318-324. https://doi.org/10.1016/j.laa.2013.10.016

@article{297d7ff4195d4050811e8d6b84d3b92c,

title = "Centralizing maps on invertible or singular matrices over division rings",

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).",

author = "Cheng-Kai Liu",

year = "2014",

month = jan,

day = "1",

doi = "10.1016/j.laa.2013.10.016",

language = "English",

volume = "440",

pages = "318--324",

journal = "Linear Algebra and Its Applications",

issn = "0024-3795",

publisher = "Elsevier Inc.",

number = "1",

}

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 -