Commuting graphs and extremal centralizers

Dolinar, Gregor; Guterman, Aleksandr Èmilevič; Kuzma, Bojan; Oblak, Polona

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Title:	Commuting graphs and extremal centralizers
Authors:	ID Dolinar, Gregor (Author) ID Guterman, Aleksandr Èmilevič (Author) ID Kuzma, Bojan (Author) ID Oblak, Polona (Author)
Files:	RAZ_Dolinar_Gregor_i2014.pdf (228,78 KB) MD5: 9CDB04635DE21D9AE1CDED8FF95C0278
Language:	English
Work type:	Unknown
Typology:	1.01 - Original Scientific Article
Organization:	ZUP - University of Primorska Press
Abstract:	We determine the conditions for matrix centralizers which can guarantee the connectedness of the commuting graph for the full matrix algebra $M_n(\mathbb{F})$ over an arbitrary field $\mathbb{F}$ . It is known that if $\mathbb{F}$ is an algebraically closed field and $n \ge 3$ , then the diameter of the commuting graph of $M_n(\mathbb{F})$ is always equal to four. We construct a concrete example showing that if $\mathbb{F}$ is not algebraically closed, then the commuting graph of $M_n(\mathbb{F})$ can be connected with the diameter at least five.
Keywords:	commuting graph, matrix ring, centralizer
Year of publishing:	2014
Number of pages:	str. 453-459
Numbering:	Vol. 7, no. 2
PID:	20.500.12556/RUP-17610
UDC:	519.17:512.6
ISSN on article:	1855-3966
COBISS.SI-ID:	16868441
Publication date in RUP:	31.12.2021
Views:	1377
Downloads:	27
Metadata:
:	DOLINAR, Gregor, GUTERMAN, Aleksandr Èmilevič, KUZMA, Bojan and OBLAK, Polona, 2014, Commuting graphs and extremal centralizers. Ars mathematica contemporanea [online]. 2014. Vol. 7, no. 2, p. 453–459. [Accessed 5 April 2025]. Retrieved from: https://repozitorij.upr.si/IzpisGradiva.php?lang=eng&id=17610 Copy citation

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Record is a part of a journal

Title:	Ars mathematica contemporanea
Publisher:	Društvo matematikov, fizikov in astronomov, Društvo matematikov, fizikov in astronomov, Univerza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologije
ISSN:	1855-3966
COBISS.SI-ID:	239049984

Secondary language

Language:	Slovenian
Title:	Grafi komutativnosti in ekstremalni cetralizatorji
Abstract:	V članku določimo pogoje na centralizatorje matrik $M_n(\mathbb{F})$ nad poljubnim obsegom $\mathbb{F}$ , ki so ekvivalentni pogoju povezanosti grafa komutativnosti $M_n(\mathbb{F})$ . Znano je, da je za algebraično zaprte obsege $\mathbb{F}$ diameter grafa komutativnosti matrične algebre $M_n(\mathbb{F})$ vsaj štiri, čim je $n \geq 3$ . Konstruiramo primer, ko je graf komutativnosti matrične algebre $M_n(\mathbb{F})$ nad nezaprtim obsegom $\mathbb{F}$ povezan z diametrom vsaj pet.
Keywords:	grafi komutativnosti, matrični kolobarji, centralizatorji

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