# $\mathbf{A}_{\text {inf}}$ has uncountable Krull dimension

24 Feb 2020 Du Heng

Let $R$ be a non-discrete rank one valuation ring of characteristic $p$ and let $\mathcal{O}_E$ be any discrete valuation ring, we prove the ring of $\mathcal{O}_E$-Witt vectors over $R$ has uncountable Krull dimension without assuming the axiom of existence of prime ideals for general commutative unitary rings...

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• NUMBER THEORY
• COMMUTATIVE ALGEBRA