Journal article
On the structure of ⋆-power conductor domains
Communications in Algebra, Vol.47(7), pp.2711-2726
2019
DOI: 10.1080/00927872.2018.1539169
Abstract
Let D be an integral domain and * a star operation defined on D. We say that D is a *-power conductor domain (*-PCD) if for each pair a, b ∈ D\(0) and for each positive integer n we have Dan ⋂ Dbn = ((Da ⋂ Db)n)*. We study *-PCDs and characterize them as root closed domains satisfying ((a, b)n)-1 = (((a, b)-1)n)* for all nonzero a, b and all natural numbers n ≥ 1. From this it follows easily that Prüfer domains are d-PCDs (where d denotes the trivial star operation), and v-domains (e.g. Krull domains) are v-PCDs. We also consider when a *-PCD is completely integrally closed, and this leads to new characterizations of Krull domains. In particular, we show that a Noetherian domain is a Krull domain if and only if it is a w-PCD. © 2018, © 2018 Taylor & Francis Group, LLC.
Details
- Title: Subtitle
- On the structure of ⋆-power conductor domains
- Creators
- D.D. Anderson - University of IowaE. Houston - University of North Carolina at CharlotteM. Zafrullah - Idaho State University
- Resource Type
- Journal article
- Publication Details
- Communications in Algebra, Vol.47(7), pp.2711-2726
- Publisher
- Taylor and Francis Inc.
- DOI
- 10.1080/00927872.2018.1539169
- ISSN
- 0092-7872
- Grant note
- DOI: 10.13039/100000893, name: Simons Foundation, award: #354565
- Language
- English
- Date published
- 2019
- Academic Unit
- Mathematics
- Record Identifier
- 9984230421502771
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