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- Title
On Almost Prüfer v-Multiplication Domains.
- Authors
Li, Qing; Tang, Zhongming
- Abstract
Let R be an integral domain and R′ the integral closure of R. In this paper, we introduce the notion of an almost Prüfer v-multiplication domain (APVMD) and continue the investigation of almost GCD-domains (AGCD-domains). We show that R is an APVMD with torsion t-class group if and only if R is an AGCD-domain. Further, we prove that R is an AGCD-domain if and only if R is a UMT-domain with torsion t-class group and R ⊆ R′ is a root extension. Finally, we discuss the polynomial ring over an almost Prüfer v-multiplication domain.
- Subjects
INTEGRAL domains; INTEGRAL closure; TORSION products; GROUP theory; POLYNOMIAL rings; ROOTS of equations; MATHEMATICAL analysis
- Publication
Algebra Colloquium, 2012, Vol 19, Issue 3, p493
- ISSN
1005-3867
- Publication type
Article
- DOI
10.1142/S1005386712000351