Commuting graphs and extremal centralizers

被引：9

作者：

Dolinar, Gregor ^{[1
]}

Guterman, Alexander ^{[2
]}

Kuzma, Bojan ^{[3
,4
]}

Oblak, Polona ^{[5
]}

机构：

[1] Univ Ljubljana, Fac Elect Engn, SI-1000 Ljubljana, Slovenia

[2] Moscow MV Lomonosov State Univ, Fac Algebra, Dept Math & Mech, Moscow 119991, Russia

[3] Univ Primorska, SI-6000 Koper, Slovenia

[4] IMFM, SI-1000 Ljubljana, Slovenia

[5] Univ Ljubljana, Fac Comp & Informat Sci, SI-1000 Ljubljana, Slovenia

来源：

ARS MATHEMATICA CONTEMPORANEA | 2014年 / 7卷 / 02期

关键词：

Commuting graph; matrix ring; centralizer; MATRIX-RINGS;

D O I：

10.26493/1855-3974.386.a83

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We determine the conditions for matrix centralizers which can guarantee the connectedness of the commuting graph for the full matrix algebra M-n (F) over an arbitrary field F. It is known that if F is an algebraically closed field and n >= 3, then the diameter of the commuting graph of M-n (F) is always equal to four. We construct a concrete example showing that if F is not algebraically closed, then the commuting graph of M-n (F) can be connected with the diameter at least five.

引用

页码：453 / 459

页数：7

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