Dp-finite and Noetherian NIP integral domains

Will Johnson

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arXiv · 2302.03315

Dp-finite and Noetherian NIP integral domains

Will Johnson

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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.

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Will Johnson. 2023-02-07. Dp-finite and Noetherian NIP integral domains. https://arxiv.org/abs/2302.03315

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