Journal article
Almost discrete valuation domains
Communications in Algebra, Vol.49(1), pp.173-184
2020
DOI: 10.1080/00927872.2020.1797069
Abstract
Let D be an integral domain. Then D is an almost valuation (AV)-domain if for (Formula presented.) there exists a natural number n with (Formula presented.) or (Formula presented.) AV-domains are closely related to valuation domains, for example, D is an AV-domain if and only if the integral closure (Formula presented.) is a valuation domain and (Formula presented.) 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 (Formula presented.) a DVR, and quasilocal and local API-domains (i.e., for (Formula presented.) there exists an n with (Formula presented.) principal). The structure of complete local AV-domains and API-domains is determined. © 2020 Taylor & Francis Group, LLC.
Details
- Title: Subtitle
- Almost discrete valuation domains
- Creators
- D.D. Anderson - University of IowaS. Xing - Chengdu University of Information TechnologyM. Zafrullah - Idaho State University
- Resource Type
- Journal article
- Publication Details
- Communications in Algebra, Vol.49(1), pp.173-184
- DOI
- 10.1080/00927872.2020.1797069
- ISSN
- 0092-7872
- Publisher
- Bellwether Publishing, Ltd.
- Language
- English
- Date published
- 2020
- Academic Unit
- Mathematics
- Record Identifier
- 9984230422002771
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