Ratliff-Rush closures of ideals with respect to a noetherian module
type: Item
instance of: scholarly article
title: Ratliff-Rush closures of ideals with respect to a noetherian module
zbMATH Open document ID: 1095.13002
author: Reza Naghipour
published in: Journal of Pure and Applied Algebra
publication date: 2005-02-23T00:00:00Z
review text: Let \(R\) be a noetherian ring, \(E\) a finitely generated \(R\)-module and \(I\) an ideal of \(R\). Assume that \(IE\neq E\) and that \(I\) contains an \(E\)-regular element. In answer to a question of \textit{W. Heinzer, B. Johnston, D. Lantz} and \textit{K. Shah} [in: Methods in module theory. Conference Colorado Springs, 1991, Lect. Notes Pure Appl. Math. 140, 149--159 (1993; Zbl 0794.13003)], the author shows that all sufficiently large powers of \(I\) are Ratliff-Rush closed with respect to \(E\). Several characterizations are also given of when all powers of \(I\) are Ratliff-Rush closed with respect to \(E\).
reviewed by: David E. Rush
Mathematics Subject Classification ID: 13A30
Mathematics Subject Classification ID: 13B22
Mathematics Subject Classification ID: 13E05
Mathematics Subject Classification ID: 13A02
zbMATH DE Number: 2137618
zbMATH Keywords: Rees ring
zbMATH Keywords: Rees module
zbMATH Keywords: associated graded ring
zbMATH Keywords: associated graded module
MaRDI profile type: Publication
full work available at URL: j.jpaa.2004.06.008
OpenAlex ID: W1996861428
cites work: Asymptotic primes and asymptotic grades on modules
cites work: Asymptotic Stability of Ass(M/I n M)
cites work: Q4274969
cites work: Q3138581
cites work: Coefficient ideals in and blowups of a commutative Noetherian domain
cites work: The ratliff-rush ideals in a noetherian ring
cites work: Q4145812
cites work: Q4451119
DOI: 10.1016/J.JPAA.2004.06.008
Recommended article: Ratliff–Rush Closure of Ideals in Pullbacks and Polynomial Rings
Recommended article: The ratliff-rush ideals in a noetherian ring
Recommended article: On Ratliff-Rush closure of modules
Recommended article: RATLIFF–RUSH CLOSURE OF IDEALS IN INTEGRAL DOMAINS
Recommended article: The Ratliff-Rush closure of initial ideals of certain prime ideals
Recommended article: Ratliff-Rush filtrations associated with ideals and modules over a Noetherian ring
Recommended article: Q3138581
Recommended article: INTEGRAL CLOSURES OF IDEALS RELATIVE TO INJECTIVE MODULES OVER COMMUTATIVE NOETHERIAN RINGS
Recommended article: Ratliff-Rush closures and coefficient modules
Recommended article: Asymptotic Primes of Ratliff–Rush Closure of Ideals with Respect to Modules
description: scientific article; zbMATH DE number 2137618