Construction, sur un anneau de Dedekind, d'une base régulière de polynômes à valeurs entières. (Construction of a regular base of integer valued polynomials over a Dedekind ring)
type: Item
instance of: scholarly article
title: Construction, sur un anneau de Dedekind, d'une base régulière de polynômes à valeurs entières. (Construction of a regular base of integer valued polynomials over a Dedekind ring)
zbMATH Open document ID: 0698.13007
DOI: 10.1007/BF01168297
author: Gilbert Gerboud
published in: Manuscripta Mathematica
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155432
review text: Using a result of \textit{P.-J. Cahen} [Can. J. Math. 24, 747-754 (1972; Zbl 0224.13006)] which characterizes Dedekind domains A such that the ring \(A[X]_{sub}\) of integer valued polynomials over A admits a basis \(Q_ 0(X),Q_ 1(X),...,Q_ n(X),..\). such that \(\deg (Q_ n(X))=n\) for any n, the author constructs explicitly such a basis. The construction depends essentially on a result of \textit{G. Pólya} which states that for such Dedekind domains and any integer n the ideal of leading coefficients of integer valued polynomials over A of degree \(\leq n\) is principal.
Mathematics Subject Classification ID: 13F20
Mathematics Subject Classification ID: 13F05
Mathematics Subject Classification ID: 11C08
zbMATH DE Number: 4144106
zbMATH Keywords: Dedekind domains
zbMATH Keywords: integer valued polynomials
reviewed by: Jiří Močkoř
MaRDI profile type: Publication
cites work: Q3843687
cites work: Q4729877
description: scientific article; zbMATH DE number 4144106