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 $D?$
A generalization of Ostrowski's Theorem
6
$\begingroup$
algebraic-number-theory
dedekind-domain
-
1In 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
1 Answers
2
If I am understanding your terminology correctly, the answer is yes: see Theorem 13 in these notes.
-
0nice. very straightforward. – 2011-06-13