20.500.12556/RUP-17610 Commuting graphs and extremal centralizers Grafi komutativnosti in ekstremalni cetralizatorji 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. 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. commuting graph matrix ring centralizer grafi komutativnosti matrični kolobarji centralizatorji true true false Angleški jezik Slovenski jezik Neznano 2021-12-31 00:31:34 2021-12-31 00:31:34 2024-03-01 14:39:19 0000-00-00 00:00:00 2014 0 0 str. 453-459 no. 2 Vol. 7 2014 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 519.17:512.6 1855-3966 16868441 RAZ_Dolinar_Gregor_i2014.pdf RAZ_Dolinar_Gregor_i2014.pdf 1 9CDB04635DE21D9AE1CDED8FF95C0278 7dcc5c7fcc1a39e073c082e9348082957a371140bed92b4ec350cbf33f1e7a81 770ffb64-c3d6-11ed-b5df-005056bf369b https://repozitorij.upr.si/Dokument.php?lang=slv&id=25917 Založba Univerze na Primorskem 0 0 0