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Classes of Bézout domains that are not EDDs

Identify and characterize classes of Bézout domains that are not elementary divisor domains (EDDs).

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Background

Beyond establishing positive criteria for the EDD property, a complementary unresolved direction is to describe and classify Bézout domains that fail to be EDDs.

The authors note that this question, posed explicitly in the literature, remains unanswered, underscoring the need for structural understanding of non-EDD Bézout domains.

References

The implicit and explicit questions raised in the literature, such as, “Is a B´ezout domain of finite Krull dimension [at least 2] an EDD?” (see [5], Ch. III, Probl. 5, p. 122), and, ‘What classes of B´ ezout domains which are not EDDs exist?’, remain unanswered.

— Matrix invertible extensions over commutative rings. Part III: Hermite rings (2405.01234 - Călugăreanu et al., 2 May 2024) in Introduction, concluding paragraph