# Reduction of matrices over simple Ore domains

## TL;DR

This paper investigates the diagonal reduction of matrices over simple Ore domains, extending existing theories to specific classes like 2-simple rings, Ore domains, and certain Bezout domains.

## Contribution

It provides new results on matrix diagonalization over simple Ore domains and related classes, broadening the understanding of their algebraic structure.

## Key findings

- Diagonal reduction techniques developed for simple Ore domains.
- Extension of results to 2-simple rings of stable range 1.
- Application to certain Bezout domains.

## Abstract

We study the theory of diagonal reductions of matrices over simple Ore domains of finite stable range. We cover the cases of 2-simple rings of stable range 1, Ore domains and certain cases of Bezout domains.