On the Diameter of the Commuting Graph of a Full Matrix Ring over a Division Ring

Abstract

For a division ring D, finite dimensional over its center F, we give a condiction for the connectedness of the commuting graph of a matrix ring over $D$. Furthermore, we prove that if the commuting graph is connected, then its diameter is between four and six.

References in corpus (1)

• Diameters of commuting graphs of matrices over semirings