Elementary matrix reduction over Bezout duo rings

TL;DR

This paper investigates conditions under which Bezout duo rings are elementary divisor rings, generalizing known results to a broader class of rings by exploring stable-like properties.

Contribution

It introduces new stable-like conditions on Bezout duo-domains that ensure they are elementary divisor rings, extending previous results to wider classes of rings.

Findings

Identification of stable-like conditions for elementary divisor rings

Generalization of known results to broader classes of rings

Conditions under which Bezout duo-domains are elementary divisor domains

Abstract

A ring $R$ is an elementary divisor ring if every matrix over $R$ admits a diagonal reduction. We further explore various stable like conditions on a bezout duo-domain under which it is an elementary divisor domain. Many known results are thereby generalized to much wider class of rings.