Commuting graphs and extremal centralizersDolinar, Gregor (Avtor) Guterman, Aleksandr Èmilevič (Avtor) Kuzma, Bojan (Avtor) Oblak, Polona (Avtor) commuting graphmatrix ringcentralizerWe 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.20142021-12-31 00:31:34Neznano17610UDK: 519.17:512.6ISSN pri članku: 1855-3966COBISS.SI-ID: 16868441sl