Skolem properties for several indeterminates
type: Item
instance of: scholarly article
zbMATH Open document ID: 0873.13017
author: Jean-Luc Chabert
publication date: 1997-11-02T00:00:00Z
Mathematics Subject Classification ID: 13F20
Mathematics Subject Classification ID: 11R54
Mathematics Subject Classification ID: 13G05
Mathematics Subject Classification ID: 13B25
zbMATH DE Number: 983068
zbMATH Keywords: integral domain
zbMATH Keywords: polynomial functions
zbMATH Keywords: Skolem property
zbMATH Keywords: order of a number field
MaRDI profile type: Publication
title: Skolem properties for several indeterminates
review text: Let \(D\) be an integral domain with quotient field \(K\), \(r\in\mathbb{N}\) and \(\text{Int} (D^r)\) the ring of \(D\)-valued polynomial functions on \(D^r\). The author investigates the so-called Skolem property for \(\text{Int} (D^r)\), which means that for each finitely generated ideal \(I\) of \(\text{Int} (D^r)\), such that \(I(a)=D\) for each \(a\in D^r\), the equality \(I= \text{Int} (D^r)\) holds -- here \(I(a)= \{f(a), f\in I\}\). The author gives a constructive proof of the already known result that \(\text{Int} (D^r)\) has that property if \(D\) is an order of a number field. Concerning the related almost strong Skolem property he derives a sufficient condition, which is fulfilled in particular for any ring of integers of a number field.NEWLINENEWLINEFor the entire collection see [Zbl 0855.00015].
reviewed by: Gerhard Kowol
description: scientific article; zbMATH DE number 983068