Let $D$ be an integrally closed domain of Krull dimension at most $2$. Is $D$ a Krull domain?
2026-03-28 23:59:12.1774742352
Is an integrally closed domain of Krull dimension at most $2$ a Krull domain?
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In fact, every valuation ring of rank two is a counterexample since Krull domains are completely integrally closed, and valuation rings are completely integrally closed iff have rank at most one.
A non-discrete valuation ring of rank one is also not a Krull domain.