# Diagonal reduction of matrices over Bezout rings of stable range 1 with the Kazimirsky condition

## TL;DR

This paper develops a theory for diagonalizing matrices over certain Bezout rings with the Kazimirsky condition, establishing conditions under which these rings are elementary divisor rings.

## Contribution

It introduces a diagonalizability theory for matrices over Bezout rings with the Kazimirsky condition and characterizes when such rings are elementary divisor rings.

## Key findings

- A ring of stable range 1 with the Kazimirsky condition is an elementary divisor ring if and only if it is a duo ring.
- The paper establishes a link between the Kazimirsky condition and elementary divisor rings.
- Provides criteria for diagonalizability over specific classes of rings.

## Abstract

We constuct the theory of diagonalizability for matrices over Bezout rings of stable range 1 with the Kazimirsky condition. It is shown that a ring of stable range 1 with the right (left) Kazimirsky condition is an elementary divisor ring if and only if it is a duo ring.