21. Commuting graphs and extremal centralizersGregor Dolinar, Aleksandr Èmilevič Guterman, Bojan Kuzma, Polona Oblak, 2014, original scientific article 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
Published in RUP: 31.12.2021; Views: 804; Downloads: 23
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25. Correction: Alao et al. Impact of Alkali and Silane Treatment on Hemp/PLA Composites' Performance: From Micro to Macro Scale. Polymers 2021, 13, 851Percy Festus Alao, Laetitia Sarah Jennifer Marrot, Michael David Burnard, Gregor Lavrič, Mart Saarna, Jaan Kers, 2021, short scientific article Keywords: hemp fibers, polylactic acid, biocomposite materials, mechanical properties, surface treatments
Published in RUP: 18.10.2021; Views: 1104; Downloads: 25
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