A commutative Bezout domain in which every maximal ideal is principal is an elementary divisor ring

TL;DR

This paper proves that a Bezout domain with all maximal ideals principal is an elementary divisor ring, advancing understanding of the structure of such algebraic domains.

Contribution

It establishes that certain Bezout domains, specifically those with principal maximal ideals, are elementary divisor rings, resolving a specific case of a longstanding problem.

Findings

Proves that Bezout domains with all maximal ideals principal are elementary divisor rings.

Clarifies the structure of specific Bezout domains.

Advances the classification of elementary divisor rings.

Abstract

In this article we revisit a problem regarding Bezout domains, namely, whether every Bezout domain is an elementary divisor domain. We prove that a Bezout domain in which every maximal ideal is principal is an elementary divisor ring