# A Bezout ring of stable range 2 which has square stable range 1

## TL;DR

This paper introduces a new class of rings with specific stable range properties and characterizes their structure, linking square stable range 1 to elementary divisor rings and Toeplitz rings.

## Contribution

It defines rings of stable range 2 with square stable range 1 and establishes their equivalence to known classes like elementary divisor rings and Toeplitz rings under certain conditions.

## Key findings

- Hermitian rings with square stable range 1 are elementary divisor rings if and only if they are duo rings of neat range 1.
- Commutative Hermitian rings are Toeplitz rings if and only if they have square stable range 1.

## Abstract

In this paper we introduced the concept of a ring of stable range 2 which has square stable range 1. We proved that a Hermitian ring $R$ which has (right) square stable range 1 is an elementary divisor ring if and only if $R$ is a duo ring of neat range 1. And we proved that a commutative Hermitian ring $R$ is a Toeplitz ring if and only if $R$ is a ring of (right) square range 1.