If $ A $, $ B $ are subrings of a field $ K $ that are Dedekind domains, is it true that $ A \cap B $ is also a Dedekind domain?
Case in point: $ \mathbb{Z}_{(3) } , \mathbb{Z}_{(5) } \subset \mathbb{Q} $ and their intersection is again a localizattion (at the complement of $ (3) \cup (5) $) which is a Dedekind domain.