arXiv:2611.14767v1 Announce Type: new Abstract: We generalize a result known for Pr\"ufer domains to show that a PVMD $R$ is completely integrally closed if and only if $\text{Inv}^t(R)$ is an archimedean $\ell$-group. It has been conjectured that a PVMD is completely integrally closed if and only if it is an Archimedean domain. It is known that a completely integrally closed PVMD is an Archimedean domain. We provide an example to illustrate that an Archimedean PVMD need not be completely integrally closed.
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