Detecting the maximal-associated prime ideal of monomial ideals
type: Item
instance of: scholarly article
title: Detecting the maximal-associated prime ideal of monomial ideals
zbMATH Open document ID: 1433.13009
author: Mehrdad Nasernejad
author: Saeed Rajaee
published in: Boletín de la Sociedad Matemática Mexicana. Third Series
publication date: 2019-11-28T00:00:00Z
review text: Let \(I\subseteq R=k[x_1,\dots,x_n]\) be a monomial ideal. The present paper provides a neccessary and sufficient condition whether the graded maximal ideal of \(R\), \(\mathfrak{m}=\langle x_1,\dots,x_n\rangle\) is in the set of associated prime ideals of \(I\), \(\mathrm{Ass}_R(R/I)\). The main result of the paper, Theorem 2.7, yields a neccessary and sufficient condition as to whether \(\mathfrak{m}\in \mathrm{Ass}_R(R/I)\) solely using the elements of the unique minimal monomial generating set of \(I\)and without computing any minimal primary decomposition of \(I\).
reviewed by: Eduardo Saenz-de-Cabezon
Mathematics Subject Classification ID: 13B25
Mathematics Subject Classification ID: 13F20
Mathematics Subject Classification ID: 13F55
Mathematics Subject Classification ID: 13D45
zbMATH DE Number: 7137969
zbMATH Keywords: associated primes
zbMATH Keywords: monomial ideals
MaRDI profile type: Publication
full work available at URL: s40590-018-0208-8
OpenAlex ID: W2818892385
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DOI: 10.1007/S40590-018-0208-8
description: scientific article; zbMATH DE number 7137969