Normality of subrings generated by square free monomials
type: Item
instance of: scholarly article
title: Normality of subrings generated by square free monomials
zbMATH Open document ID: 0862.13008
DOI: 10.1016/0022-4049(95)00145-X
author: Rafael H. Villarreal
published in: Journal of Pure and Applied Algebra
publication date: 1997-05-25T00:00:00Z
review text: Let \(\{x_1, \dots, x_n\}\) be the vertex set of a graph \(G\); the ideal \(I(G)\) generated by all the monomials \(x_ix_j\), where \(\{x_i, x_j\}\) is an edge in \(G\), is called the edge ideal of \(G\); \(I(G)\) is a square-free homogeneous ideal, generated in degree 2 and \(G\) is normal if the Rees algebra of \(I(G)\) is normal. The author proves here some results on ideals generated by square free monomials which, in the previous setting, imply that when a graph \(G\) is normal, then also the cone over \(G\) and the suspension of \(G\) are normal. Applications and extensions in the case \(G\) = complete graph are considered.
reviewed by: Luca Chiantini
Mathematics Subject Classification ID: 13F20
Mathematics Subject Classification ID: 05E99
Mathematics Subject Classification ID: 13H10
zbMATH DE Number: 943213
zbMATH Keywords: edge ideal
zbMATH Keywords: monomials
MaRDI profile type: Publication
cites work: Q4305609
cites work: Normal Rees algebras
cites work: Q4274969
cites work: Q3714165
cites work: \(M\)-sequences, graph ideals, and ladder ideals of linear type
cites work: R-SEQUENCES AND INDETERMINATES
cites work: Cohen-Macaulay Rees algebras and their specialization
cites work: Torus orbits in \(G/P\)
cites work: Arithmetic of normal Rees algebras
cites work: Rings of Invariants of Tori, Cohen-Macaulay Rings Generated by Monomials, and Polytopes
cites work: Toroidal embeddings. I
cites work: Gröbner bases and triangulations of the second hypersimplex
cites work: Q5611879
cites work: On the ideal theory of graphs
cites work: Gröbner bases of toric varieties
cites work: ASYMPTOTIC ANALYSIS OF TORIC IDEALS
cites work: Q4861423
cites work: On cohen-macaulay simplicial complexes
cites work: Derivations of commutative noetherian rings
cites work: Rees algebras of edge ideals
description: scientific article; zbMATH DE number 943213