On low Gorenstein colength
type: Item
instance of: scholarly article
title: On low Gorenstein colength
zbMATH Open document ID: 1403.13039
published in: Journal of Algebra
publication date: 2018-09-24T00:00:00Z
review text: Let \(A = R/I\) be a quotient of the ring \(R = kx_1,\dots,x_n\) of formal power series, for some \(n \geq 1\), where \(k\) is a field. The ring \(A\) is \textit{Teter} if \(A\) has the form \(G / \text{soc}(G)\), where \(G\) is Gorenstein. The \textit{Gorenstein colength} \(\text{gcl}(A)\) is defined as the minimum of \(\ell (G) - \ell(A)\), where \(G\) is an Artin Gorenstein ring such that \(A \cong G/H\) for some ideal \(H \subset G\). We know that \(A\) is Teter if and only if \(\text{gcl}(A) = 1\). The goal of this paper is to extend and improve the characterization of Artin rings \(A = R/I\) of Gorenstein colength two due to H. Ananthnarayan, and to extend the characterization of Teter rings given by the first author and M. Silva-Takatuji to Artin rings of Gorenstein colength two. Both improvements are in terms of their Macaulay inverse systems \(I^\perp\). In particular, the authors give an explicit generator of \(I^\perp\). They also give several explicit examples and families of Gorenstein colength two rings in terms of their analytic type.
reviewed by: Juan C. Migliore
Mathematics Subject Classification ID: 13H10
Mathematics Subject Classification ID: 13H15
Mathematics Subject Classification ID: 14C05
zbMATH DE Number: 6942903
zbMATH Keywords: Gorenstein rings
zbMATH Keywords: Artin rings
zbMATH Keywords: Macaulay's inverse system
zbMATH Keywords: Hilbert function
zbMATH Keywords: Gorenstein colength
author: J. Elias
author: Roser Homs
describes a project that uses: Inverse-syst
describes a project that uses: SINGULAR
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2018.07.016
OpenAlex ID: W2885789092
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Wikidata QID: Q129440058
DOI: 10.1016/J.JALGEBRA.2018.07.016
description: scientific article; zbMATH DE number 6942903