Submission date: 7 February 2023

Abstract:

We prove some results on NIP integral domains, especially those that are Noetherian or have finite dp-rank. If R is an NIP Noetherian domain that is not a field, then R is a semilocal ring of Krull dimension 1, and the fraction field of R has characteristic 0. Assuming the henselianity conjecture (on NIP valued fields), R is a henselian local ring. Additionally, we show that integral domains of finite dp-rank are henselian local rings. Finally, we lay some groundwork for the study of Noetherian domains of finite dp-rank, and we classify dp-minimal Noetherian domains.

Mathematics Subject Classification: 03C60

Keywords and phrases:

Full text arXiv 2302.03315: pdf, ps.