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arXiv · 2405.21014

The classification of dp-minimal integral domains

Christian d'Elbée·Yatir Halevi·Will Johnson
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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 O extending R, a proper ideal I in O, and a finite subring S in O/I such that R is the preimage of S in O.

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Christian d'Elbée, Yatir Halevi, Will Johnson. 2024-05-31. The classification of dp-minimal integral domains. https://doi.org/10.2140/mt.2025.4.131

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