Autor:	Johnson, Will
Rok vydání:	2023
Předmět:	Mathematics - Logic Mathematics - Commutative Algebra 03C60
Druh dokumentu:	Working Paper
Popis:	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. Comment: 23 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2302.03315 Zobrazit plný text záznamu View this record from Arxiv