Generating ideals in rings of integer-valued polynomials
type: Item
instance of: scholarly article
title: Generating ideals in rings of integer-valued polynomials
zbMATH Open document ID: 0589.12002
DOI: 10.1016/0021-8693(85)90129-2
published in: Journal of Algebra
publication date: 1985-01-01T00:00:00Z
review text: Let K be an algebraic number field with integers A. The author considers the subring of the polynomial ring K[X] consisting of the polynomials for which f(A)\(\subseteq A\). For this ring of ''integer-valued polynomials'' the author proves that every finitely generated ideal can be generated by two elements. This extends a result by \textit{R. Gilmer} and the reviewer [J. Algebra 81, 150-164 (1983; Zbl 0515.13016)] for the case K being the rational numbers. An additional extension of this result to a more general class of Dedekind domains can be found in a paper by \textit{D. L. McQuillan} [J. Reine Angew. Math. 358, 162-178 (1985; Zbl 0568.13003)].
Mathematics Subject Classification ID: 11R09
Mathematics Subject Classification ID: 13F20
Mathematics Subject Classification ID: 13A15
zbMATH DE Number: 3946266
zbMATH Keywords: algebraic number field
zbMATH Keywords: integer-valued polynomials
zbMATH Keywords: finitely generated ideal
author: David E. Rush
MaRDI profile type: Publication
full work available at URL: 0021-8693(85)90129-2
OpenAlex ID: W2043089180
cites work: Hilbert rings of integral-valued polynomials
cites work: A theorem on ideals in prüfer rings of integral-valued polynomials
cites work: Polynomes a Valeurs Entieres
cites work: On the number of generators of an invertible ideal
cites work: Finitely generated ideals of the ring of integer-valued polynomials
description: scientific article; zbMATH DE number 3946266