Asymptotic closure of filtrations on rings with Krull dimension 1
type: Item
instance of: scholarly article
title: Asymptotic closure of filtrations on rings with Krull dimension 1
zbMATH Open document ID: 0897.13011
author: H. Dichi
author: D. Sangare
published in: Archiv der Mathematik
publication date: 1998-04-26T00:00:00Z
review text: In the present paper, the concept of asymptotic closure \(\overline {(f,M)}\) of a filtration \(f\) relative to a module \(M\) is introduced and investigated. The methods used by the authors in previous notes on integral and prüferian closure operations of a filtration prove to be efficient here, despite the complexity of the asymptotic closure operation comparatively to the integral and prüferian closure operation. Our main result gives a complete description of the asymptotic closure \(\overline f\) of a filtration \(f\) on a Dedekind ring \(A\), in terms of the prime ideals of which \(\sqrt f\) is the product, when \(f\) belongs to some class containing noetherian filtrations.
Mathematics Subject Classification ID: 13B99
Mathematics Subject Classification ID: 13F05
zbMATH DE Number: 1145414
zbMATH Keywords: asymptotic closure
zbMATH Keywords: Dedekind ring
zbMATH Keywords: noetherian filtrations
MaRDI profile type: Publication
full work available at URL: s000130050148
OpenAlex ID: W2093552733
DOI: 10.1007/S000130050148
description: scientific article; zbMATH DE number 1145414