266 KB18 KB200820252014Dolinar, GregorGuterman, Aleksandr EmilevičKuzma, BojanOblak, Polonaštevilka:2letnik:7str. 453-459COBISSID:16868441ISSN:1855-3966URN:URN:NBN:SI:doc-910J6R1JenDruštvo matematikov, fizikov in astronomov SlovenijeArs mathematica contemporaneacentralizatorjicentralizercommuting graphgrafi komutativnostimatrični kolobarjimatrix ringCommuting graphs and extremal centralizers|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 fiveV 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 petTEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije