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Commuting graphs and extremal centralizers
Dolinar, Gregor, 11.08.1971- ...
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.
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