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 › peer-review

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

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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).",

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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).

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