Full subsets of a noetherian ring
type: Item
instance of: scholarly article
title: Full subsets of a noetherian ring
zbMATH Open document ID: 0780.13013
author: Paul-Jean Cahen
published in: Journal of Algebra
publication date: 1994-01-30T00:00:00Z
review text: A subset \(E\) of a domain \(R\) is called ``full'' if for each \(P\in R[X]\) such that \(P(E)\subset\mathbb{Z}\) it follows that \(P(\mathbb{Z})\subset\mathbb{Z}\). If \(R\) is a \(D\)-ring which is noetherian and 1-dimensional, such that, for each maximal ideal \({\mathfrak m}\), \(R/{\mathfrak m}\) is finite and the localization \(R_{\mathfrak m}\) is analytically irreducible, then a subset \(E\) of \(R\) is full if and only if \(E\) is dense in the \({\mathfrak m}\)-adic topology, for each maximal ideal \({\mathfrak m}\).
Mathematics Subject Classification ID: 13F20
Mathematics Subject Classification ID: 13E05
Mathematics Subject Classification ID: 13G05
zbMATH DE Number: 202990
zbMATH Keywords: full subset
zbMATH Keywords: integer valued polynomials
reviewed by: Serban Raianu
MaRDI profile type: Publication
full work available at URL: jabr.1993.1097
OpenAlex ID: W2034028935
DOI: 10.1006/JABR.1993.1097
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description: scientific article; zbMATH DE number 202990