N-rings and ACC on colon ideals
type: Item
instance of: scholarly article
title: N-rings and ACC on colon ideals
zbMATH Open document ID: 0577.13012
DOI: 10.1016/0022-4049(84)90047-1
published in: Journal of Pure and Applied Algebra
publication date: 1984-01-01T00:00:00Z
review text: \textit{R. Gilmer} and \textit{W. Heinzer} [cf. ibid. 24, 123-144 (1982; Zbl 0495.13002)] introduced the notion of N-ring, that is, a ring R such that, for every ideal A of R, there exists a Noetherian ring extension S of R such that \(AS\cap R=A\). Although an N-ring need not be Noetherian (an example attributed to M. Hochster, of a one-dimensional quasilocal non- Noetherian integral domain which is an N-ring is given here), in this paper the authors show that such a ring shares many of the usual properties of a Noetherian ring. For instance, every finite integral extension of an N-ring is an N-ring. This result is a consequence of one of the main theorems of this paper: A ring R is an N-ring if and only if, for every ideal A of R, the ring R/A satisfies the ascending chain condition on annihilator ideals.
Mathematics Subject Classification ID: 13E05
Mathematics Subject Classification ID: 13B02
Mathematics Subject Classification ID: 13E99
zbMATH DE Number: 3922817
zbMATH Keywords: noetherianness
zbMATH Keywords: colon ideals
zbMATH Keywords: N-ring
zbMATH Keywords: ascending chain condition on annihilator ideals
author: William J. Heinzer
author: David C. Lantz
MaRDI profile type: Publication
full work available at URL: 0022-4049(84)90047-1
OpenAlex ID: W2058549789
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description: scientific article; zbMATH DE number 3922817