A note on commuting graphs of matrix rings over fields

Abstract

We will give a short proof of the fact that if the algebraic closure of a field $\mathbb{F}$ is a finite extension, then for $n\ge 3$ the commuting graph $\Gamma (M_n(\mathbb{F}))$ is connected and its diameter is four.

References in corpus (3)

• A matrix ring with commuting graph of maximal diameter
• Diameters of commuting graphs of matrices over semirings
• On the diameter of the commuting graph of the full matrix ring over the real numbers

Cited by in corpus (1)

• A matrix ring with commuting graph of maximal diameter