Tight double linkage of Gorenstein algebras
type: Item
instance of: scholarly article
title: Tight double linkage of Gorenstein algebras
zbMATH Open document ID: 0568.13006
DOI: 10.1016/0021-8693(85)90110-3
author: Andrew Kustin
author: M. P. Miller
published in: Journal of Algebra
publication date: 1985-01-01T00:00:00Z
review text: A Gorenstein ideal K in a local ring R is in the class \({\mathcal H}\) if there is a sequence of linked ideals \(I_ 0\sim I_ 1\sim...\sim I_{2n}=K\) with \(I_ 0\) a complete intersection and \(I_{2i}\) Gorenstein for all i. If K is in \({\mathcal H}\), then K is linked to a complete intersection by a sequence of ''tight double links.'' This means there is a sequence \(I_ 0=J_ 0\sim J_ 1\sim...\sim J_{2m}=K\), such that for each p, \(J_{2p+1}\) is an almost complete intersection of the form (\({\mathfrak b},y,w)\) and its immediate neighbors are linked to it by the ''similar'' regular sequences (\({\mathfrak b},y)\) and (\({\mathfrak b},w)\), respectively. In this sense \(J_{2p}\) and \(J_{2p+2}\) are ''tightly linked'' Gorenstein ideals. Let k be an algebraically closed field and \(A=kX_ 1,...,X_ q/K\) with K in \({\mathcal H}\). The k-algebra A is rigid if and only if it is linked to a regular complete intersection by a sequence of semi-generic tight double links. It follows that if A is rigid, then it is regular in codimension six.
Mathematics Subject Classification ID: 13H10
Mathematics Subject Classification ID: 14M05
Mathematics Subject Classification ID: 13D10
zbMATH DE Number: 3906614
zbMATH Keywords: tight double linkage
zbMATH Keywords: rigid algebra
zbMATH Keywords: Gorenstein ideal
zbMATH Keywords: almost complete intersection
MaRDI profile type: Publication
full work available at URL: 0021-8693(85)90110-3
OpenAlex ID: W2004534086
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description: scientific article; zbMATH DE number 3906614