Alexander duality for Stanley-Reisner rings and squarefree \(\mathbb{N}^n\)-graded modules
type: Item
instance of: scholarly article
title: Alexander duality for Stanley-Reisner rings and squarefree \(\mathbb{N}^n\)-graded modules
zbMATH Open document ID: 0981.13011
author: Kohji Yanagawa
published in: Journal of Algebra
publication date: 2002-03-07T00:00:00Z
review text: This paper introduces the notion of squarefree modules which generalizes Stanley-Reisner rings and which includes their syzygies and Ext modules. For a squarefree module the author constructs a chain complex of free modules, which is acyclic if the given module is Cohen-Macaulay. This complex is very convenient for the study of the Alexander duality. As a consequence, the author obtains results on the minimal resolutions of Stanley-Reisner rings which recover recent results of Herzog and others on componentwise linear ideals. The readers are advised to look also at recent related works on Alexander duality by \textit{E. Miller} [J. Algebra 231, 180-234 (2000; Zbl 0968.13009)] and \textit{T. Römer} [Osaka J. Math. 38, 469-485 (2001; see the following review Zbl 0981.13012].
reviewed by: Trung Ngo Viet
Mathematics Subject Classification ID: 13F55
Mathematics Subject Classification ID: 13C14
Mathematics Subject Classification ID: 13D02
Mathematics Subject Classification ID: 13D07
zbMATH DE Number: 1429461
zbMATH Keywords: minimal resolutions of Stanley-Reisner rings
zbMATH Keywords: squarefree module
zbMATH Keywords: Alexander duality
zbMATH Keywords: canonical module
MaRDI profile type: Publication
full work available at URL: jabr.1999.8130
OpenAlex ID: W1976534062
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DOI: 10.1006/JABR.1999.8130
description: scientific article; zbMATH DE number 1429461