I saw a questions in a book (that unfortunately I don't remember it's name!) and couldn't solve it.
What are Archimedean and non-Archimedean valuations of the field $\mathbb{Q}(\sqrt[3]{2})$?
2026-03-26 20:39:35.1774557575
valuations of $\mathbb{Q}(\sqrt[3]{2})$
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This is asking for an analogue in $\mathbf Q(\sqrt[3]{2})$ of Ostrowski's theorem for $\mathbf Q$. See Theorem 3.3 here for Ostrowski's theorem in every number field.