Let $K$ be a global field and let $S$ be a finite, nonempty set of places of $K$ containing the infinite one. Show that $R_S (=K \cap A_{K,S})$, the ring of $S$-integers of $K$, is a Dedekind domain. (Here $A_{K,S}$ is the ring of $S$-adeles.)
2026-03-25 03:01:49.1774407709
$R_S (=K \cap A_{K,S})$ is a Dedekind domain
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