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Almost discrete valuation domains
Communications in Algebra ( IF 0.6 ) Pub Date : 2020-08-04 , DOI: 10.1080/00927872.2020.1797069
D. D. Anderson 1 , Shiqi Xing 2 , Muhammad Zafrullah 3
Affiliation  

Abstract Let D be an integral domain. Then D is an almost valuation (AV)-domain if for there exists a natural number n with or AV-domains are closely related to valuation domains, for example, D is an AV-domain if and only if the integral closure is a valuation domain and is a root extension. In this note, we explore various generalizations of DVRs (which we might call almost DVRs) such as Noetherian AV-domains, AV-domains with a DVR, and quasilocal and local API-domains (i.e., for there exists an n with principal). The structure of complete local AV-domains and API-domains is determined.

中文翻译:

几乎离散的估值域

Abstract 令 D 是一个整数域。则 D 是一个几乎估值(AV)域,如果存在一个自然数 n 或 AV 域与估值域密切相关,例如,D 是一个 AV 域,当且仅当积分闭包是一个估值域并且是根扩展名。在这篇笔记中,我们探索了 DVR(我们可以称之为几乎 DVR)的各种概括,例如 Noetherian AV 域、带有 DVR 的 AV 域以及准本地和本地 API 域(即,因为存在一个带有主体的 n) . 确定完整的本地 AV 域和 API 域的结构。
更新日期:2020-08-04
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