Asymptotic behaviour of monomial ideals on regular sequences
type: Item
instance of: scholarly article
title: Asymptotic behaviour of monomial ideals on regular sequences
zbMATH Open document ID: 1115.13016
DOI: 10.4171/RMI/479
author: Monireh Sedghi
published in: Revista Matemática Iberoamericana
publication date: 2007-05-03T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.rmi/1169480036
full work available at URL: https://eudml.org/doc/41998
review text: Summary: Let \(R\) be a commutative noetherian ring, and let \({\mathbf x}= x_1,\dots, x_d\) be a regular \(R\)-sequence contained in the Jacobson radical of \(R\). An ideal \(I\) of \(R\) is said to be a monomial ideal with respect to \({\mathbf x}\) if it is generated by a set of monomials \(x^{e_1}_1\cdots x^{e_d}_d\). The monomial closure of \(I\), denoted by \(\widetilde I\), is defined to be the ideal generated by the set of all monomials \(m\) such that \(m^n\in I^n\) for some \(n\in\mathbb{N}\). It is shown that the sequences \(\text{Ass}_R R/\widetilde{I^n}\) and \(\text{Ass}_R\widetilde{I^n}/I^n\), \(n= 1,2,\dots\), of associated prime ideals are increasing and ultimately constant for large \(n\). In addition, some results about the monomial ideals and their integral closures are included.
Mathematics Subject Classification ID: 13B22
Mathematics Subject Classification ID: 13B21
Mathematics Subject Classification ID: 13D45
Mathematics Subject Classification ID: 13A15
Mathematics Subject Classification ID: 13E05
zbMATH DE Number: 5149124
zbMATH Keywords: monomial ideals
zbMATH Keywords: integral closures
zbMATH Keywords: monomial closures
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5149124