Commuting graphs and extremal centralizers

Authors

  • Gregor Dolinar
  • Alexander Guterman
  • Bojan Kuzma
  • Polona Oblak

DOI:

https://doi.org/10.26493/1855-3974.386.a83

Keywords:

Commuting graph, matrix ring, centralizer.

Abstract

We determine the conditions for matrix centralizers which can guarantee the connectedness of the commuting graph for the full matrix algebra Mn(F) over an arbitrary field F. It is known that if F is an algebraically closed field and n ≥ 3, then the diameter of the commuting graph of Mn(F) is always equal to four. We construct a concrete example showing that if F is not algebraically closed, then the commuting graph of Mn(F) can be connected with the diameter at least five.

Published

2013-12-26

Issue

Section

Articles