The Picard group of an integer-valued polynomial ring
type: Item
instance of: scholarly article
title: The Picard group of an integer-valued polynomial ring
zbMATH Open document ID: 0776.13008
DOI: 10.1016/S0021-8693(05)80057-2
author: Jean-Luc Chabert
published in: Journal of Algebra
publication date: 1992-09-27T00:00:00Z
review text: Let \(A\) be a one dimensional noetherian domain with finite residue fields. The author study the Picard group of the ring \(B=\{f \in K[X]|\) \(f(a) \in A\) for all \(a \in A\}\) of integer valued polynomials over \(A\). First he reduces the problem to the local ring case, then he proves that \(\text{Pic}(B)\) is isomorphic to the class group \({\mathcal C}(A,{\mathcal P}(A))/{\mathcal P}(A)\) of locally constant functions from \(A\) to the group \({\mathcal P}(A)\) of principal fractional ideals of \(A\) if and only if the \(m\)-adic completion \(A^*\) is a domain. Special cases of this result were known, for example when the ring \(A\) is a countable set.
reviewed by: Marcel Morales
Mathematics Subject Classification ID: 13C20
Mathematics Subject Classification ID: 13F20
Mathematics Subject Classification ID: 14C22
zbMATH DE Number: 63902
zbMATH Keywords: Picard group
zbMATH Keywords: integer valued polynomials
zbMATH Keywords: class group
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 63902