When is an N-ring Noetherian?
type: Item
instance of: scholarly article
title: When is an N-ring Noetherian?
zbMATH Open document ID: 0577.13013
DOI: 10.1016/0022-4049(86)90140-4
published in: Journal of Pure and Applied Algebra
publication date: 1986-01-01T00:00:00Z
review text: A ring (resp. domain) R is called an N-ring (domain) if for each ideal I in R there is a Noetherian ring (domain) T, \(\supseteq R\), such that \(IT\cap R=I\). These concepts were introduced by \textit{R. Gilmer} and \textit{W. Heinzer} [J. Pure Appl. Algebra 24, 123-144 (1982; Zbl 0495.13002)]. Substantial comment is made on these and related ring conditions (Laskerian, Mori, etc.). The question of the title leads the authors to obtain conditions for an intersection of 1-dimensional local Noetherian domains to be Noetherian. Highlight of the paper is perhaps the development of an example by Hochster, cited by the authors in J. Pure Appl. Algebra 32, 115-127 (1984; see the preceding review), to obtain a 1-dimensional quasilocal domain which is an N-ring but not an N-domain.
Mathematics Subject Classification ID: 13E05
Mathematics Subject Classification ID: 13B02
Mathematics Subject Classification ID: 13E99
zbMATH DE Number: 3922818
zbMATH Keywords: Mori domain
zbMATH Keywords: Laskerian domain
zbMATH Keywords: N-ring
zbMATH Keywords: Noetherian ring
author: William J. Heinzer
author: David C. Lantz
reviewed by: C. P. L. Rhodes
MaRDI profile type: Publication
full work available at URL: 0022-4049(86)90140-4
OpenAlex ID: W2018018750
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description: scientific article; zbMATH DE number 3922818