6 problems

Let $D$ be a Prüfer domain. A locally principal ideal of $D$ is an ideal that becomes principal upon localization at every maximal ideal, and $D$ is of finite character if every no…

Bézout-domain conjecture. If $R$ satisfies property $\mathrm{ID}_2$, then $R$ is a Bézout domain.

Integral-closedness criterion. If $\operatorname{Int}_K(A)$ is integrally closed, then $\operatorname{Int}_K(A)$ is Prüfer.

Let $D$ be a strongly discrete Prüfer domain, and let $\mathrm{Inv}(D)$ denote its group of invertible ideals. Freeness conjecture. If $D$ is a strongly discrete Prüfer domain, the…

Let $R$ be a Prüfer domain and let $\lambda$ be a limit ordinal. The Ziegler-spectrum CB-rank conjecture. There does not exist a Prüfer domain whose Ziegler spectrum has Cantor–Ben…

Archimedean characterization conjecture. $D$ is completely integrally closed if and only if $D$ is Archimedean.