Asymptotic primes and asymptotic grades on modules
type: Item
instance of: scholarly article
title: Asymptotic primes and asymptotic grades on modules
zbMATH Open document ID: 0841.13002
author: Sung Hun Ahn
published in: Journal of Algebra
publication date: 1996-07-14T00:00:00Z
review text: The aim of this paper is to study various questions related to sets of prime ideals associated to powers of an ideal \(I\) of a commutative Noetherian ring with identity \(R\) and a finitely generated \(R\)-module \(M\). In several recent papers (mid '80), \textit{D. Katz}, \textit{S. McAdam}, \textit{J. L. Ratliff}, and co-workers have introduced and developed the concepts of asymptotic (resp. essential) prime divisors, asymptotic (resp. essential) sequences, and asymptotic (resp. essential) grades associated to ideals of commutative Noetherian rings, and established some of their basic properties. In the paper under review the author extends these concepts and results from rings to modules.
Mathematics Subject Classification ID: 13A30
Mathematics Subject Classification ID: 13E05
zbMATH DE Number: 783900
zbMATH Keywords: asymptotic prime
zbMATH Keywords: essential sequences
zbMATH Keywords: asymptotic grades
zbMATH Keywords: prime divisors
zbMATH Keywords: Noetherian rings
reviewed by: Toma Albu
MaRDI profile type: Publication
full work available at URL: jabr.1995.1163
OpenAlex ID: W2075048879
DOI: 10.1006/JABR.1995.1163
description: scientific article; zbMATH DE number 783900