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Let $D$ be a Dedekind domain and $|\cdot|$ be a bounded, nontrivial norm on $D.$ Is $|\cdot|$ equivalent to an $I$-adic norm for some maximal ideal $I$ of $D?$

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    In the case that the class group of $D$ is torsion, a standard proof for Ostrowski's theorem (say in koblitz) can be adapted to prove the above result.2011-06-12

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If I am understanding your terminology correctly, the answer is yes: see Theorem 13 in these notes.

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    nice. very straightforward.2011-06-13