Yet another solution to the Burnside problem for matrix semigroups

TL;DR

This paper introduces a new proof that finitely generated periodic matrix semigroups are finite, using the kernel category to establish a finiteness condition for semigroups.

Contribution

It provides a novel proof of a known result about matrix semigroups using the kernel category approach.

Findings

Finitely generated periodic matrix semigroups are finite.

Kernel category offers a new perspective for semigroup finiteness conditions.

Abstract

We use the kernel category to give a finiteness condition for semigroups. As a consequence we provide yet another proof that finitely generated periodic semigroups of matrices are finite.