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Classes of Bézout domains that are not EDDs

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

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Background

While the paper gives multiple criteria for a Hermite ring or Bézout domain to be an EDR/EDD, it also notes that the task of delineating classes of Bézout domains that fail to be EDDs is still unresolved in the literature.

Clarifying and constructing such classes would sharpen the boundary of the EDD property within Bézout domains and complement the positive criteria developed in the paper.

References

The implicit and explicit questions raised in the literature, such as, "Is a Bezout domain of finite Krull dimension [at least 2] an EDD?" (see [5], Ch. III, Probl. 5, p. 122), and, 'What classes of Bezout 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 Section 1 (Introduction), following Criterion 1.22