Mori domains of integer-valued polynomials
type: Item
instance of: scholarly article
title: Mori domains of integer-valued polynomials
zbMATH Open document ID: 0978.13010
DOI: 10.1016/S0022-4049(99)00073-0
author: Paul-Jean Cahen
author: Stefania Gabelli
author: Evan Houston
published in: Journal of Pure and Applied Algebra
publication date: 2002-02-04T00:00:00Z
review text: The authors deal with the problem under which conditions the ring \[ \text{Int} (D)=\{f\in K[X]; f(D)\subseteq D\} \] of integer-valued polynomials over a domain \(D\) with quotient field \(K\) is a Mori domain. If \(D\) is e.g. a Krull domain or a one-dimensional Noetherian domain this question is answered completely because in this case holds: \(\text{Int} (D)=D[X]\) (corollary 2.7 and theorem 3.1). The construction of a domain \(D\) with \(\text{Int} (D)\neq D[X]\) and \(\text{Int} (D)\) a Mori domain is given in \S 3. Further investigations concern the class group of \(\text{Int}(D)\).
reviewed by: Gerhard Kowol
Mathematics Subject Classification ID: 13F20
Mathematics Subject Classification ID: 13C20
Mathematics Subject Classification ID: 13G05
zbMATH DE Number: 1526259
zbMATH Keywords: integer valued polynomials
zbMATH Keywords: Mori domain
zbMATH Keywords: class group
zbMATH Keywords: pseudo-valuation domain
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1526259