3 problems

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

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.