Abstract

We classify dp-minimal integral domains, building off the existing classification of dp-minimal fields and dp-minimal valuation rings. We show that if $R$ is a dp-minimal integral domain, then $R$ is a field or a valuation ring or arises from the following construction: there is a dp-minimal valuation overring $\mathcal{𝒪}\supseteq R$, a proper ideal $I$ in $\mathcal{𝒪}$, and a finite subring $R_0\subseteq \mathcal{𝒪}∕I$ such that $R$ is the preimage of $R_0$ in $\mathcal{𝒪}$.

Keywords

Mathematical Subject Classification

Milestones

Authors