Submission date: 31 May 2024

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.

Mathematics Subject Classification: 03C45

Keywords and phrases:

Full text arXiv 2405.21014: pdf, ps.