On the class group of integer-valued polynomial rings over Krull domains
type: Item
instance of: scholarly article
title: On the class group of integer-valued polynomial rings over Krull domains
zbMATH Open document ID: 0966.13015
DOI: 10.1016/S0022-4049(98)00159-5
author: Stefania Gabelli
author: Francesca Tartarone
published in: Journal of Pure and Applied Algebra
publication date: 2001-08-12T00:00:00Z
review text: This paper focusses on the property when the class group of a domain is generated by the classes of \(t\)-invertible \(t\)-prime ideals, which holds for Krull domains. On the one hand the authors derive a necessary and sufficient condition for arbitrary domains to possess this property. On the other hand they investigate in this respect the integer-valued polynomial ring over a Krull domain \(D\), \(\text{Int}(D)=\{f\in K[X];f(D)\subseteq D\}\) \((K\) being the quotient field of \(D)\). For example, \(\text{Int}(D)\) has that property if \(D\) has at most finitely many height-one primes with finite residue fields (corollary 2.1).
reviewed by: Gerhard Kowol
Mathematics Subject Classification ID: 13F20
Mathematics Subject Classification ID: 13C20
Mathematics Subject Classification ID: 13A15
Mathematics Subject Classification ID: 13F05
zbMATH DE Number: 1462309
zbMATH Keywords: invertible ideal
zbMATH Keywords: \(t\)-prime ideals
zbMATH Keywords: class group
zbMATH Keywords: integer-valued polynomial ring
zbMATH Keywords: Krull domain
MaRDI profile type: Publication
Wikidata QID: Q127741224
description: scientific article; zbMATH DE number 1462309