Presentations of matrix rings

TL;DR

This paper provides a concise presentation of the matrix ring of n x n matrices over Z using only two generators and three relations, simplifying its algebraic description.

Contribution

It introduces a minimal presentation of matrix rings over Z with a small set of generators and relations, enhancing understanding of their algebraic structure.

Findings

Matrix rings over Z can be generated by two elements.

Only three relations are needed to define the ring.

The presentation simplifies the algebraic understanding of matrix rings.

Abstract

We construct a short presentation of the ring of n x n matrices over Z with only 2 generators and 3 relations.