Journal article
Completely integrally closed Prüfer v-multiplication domains
Communications in Algebra, Vol.45(12), pp.5264-5282
2017
DOI: 10.1080/00927872.2017.1303502
Abstract
We study the effects on D of assuming that the power series ring D[[X]] is a v-domain or a Prüfer v-multiplication domain (PVMD). We show that a PVMD D is completely integrally closed if and only if ∩n=1∞(In)v = (0) for every proper t-invertible t-ideal I of D. Using this, we show that if D is an almost GCD domain, then D[[X]] is integrally closed if and only if D is a completely integrally closed PVMD with torsion t-class group. We also determine several classes of PVMDs for which being Archimedean is equivalent to being completely integrally closed and give some new characterizations of integral domains related to Krull domains. © 2017 Taylor & Francis.
Details
- Title: Subtitle
- Completely integrally closed Prüfer v-multiplication domains
- Creators
- D.D. Anderson - University of IowaD.F. Anderson - University of Tennessee at KnoxvilleM. Zafrullah - Idaho State University
- Resource Type
- Journal article
- Publication Details
- Communications in Algebra, Vol.45(12), pp.5264-5282
- Publisher
- Taylor and Francis Inc.
- DOI
- 10.1080/00927872.2017.1303502
- ISSN
- 0092-7872
- Language
- English
- Date published
- 2017
- Academic Unit
- Mathematics
- Record Identifier
- 9984230627902771
Metrics
3 Record Views