# J-Noetherian Bezout domain which is not a ring of stable range 1

## TL;DR

This paper investigates a specific class of algebraic structures called J-Noetherian Bezout domains, demonstrating the existence of a nonunit adequate element in such domains that are not of stable range 1.

## Contribution

It provides the first example of a J-Noetherian Bezout domain lacking stable range 1 with a nonunit adequate element.

## Key findings

- Existence of nonunit adequate element in certain Bezout domains
- J-Noetherian Bezout domains can lack stable range 1
- New insights into the structure of Bezout domains

## Abstract

We proved that in J-Noetherian Bezout domain which is not a ring of stable range 1 exists a nonunit adequate element (element of almost stable range 1