EDD property for Bézout domains of finite Krull dimension

Determine whether every Bézout domain of finite Krull dimension—particularly those of Krull dimension at least 2—is an elementary divisor domain (EDD).

Background

The paper develops new and refined criteria for when Hermite rings and, in particular, Bézout domains are elementary divisor rings/domains (EDR/EDD). Despite these advances, the authors highlight that a longstanding question from the literature—posed, for example, in Fuchs and Salce, Modules over non-Noetherian domains (Ch. III, Problem 5)—remains unresolved.

The question asks whether finiteness of Krull dimension for a Bézout domain forces it to be an elementary divisor domain, with some formulations focusing specifically on the case of Krull dimension at least 2. The authors’ results provide new tools and criteria but do not settle this global structural question.