The Gorenstein property depends on characteristic
type: Item
instance of: scholarly article
title: The Gorenstein property depends on characteristic
zbMATH Open document ID: 0549.13005
author: Hans-Gert Gräbe
published in: Beiträge zur Algebra und Geometrie
publication date: 1984-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/138270
review text: Using the characterization of the Gorenstein property of Stanley-Reisner rings in terms of the homology groups of the underlying simplicial complex and the dependence of the latter on the characteristic of the ground field k the author gives an example of a Stanley-Reisner ring k[\(\Delta]\) that is Gorenstein for \(char k\neq 2\) and not for \(char k=2.\) A theorem shows that k[\(\Delta]\) being Cohen-Macaulay over any field and Gorenstein over some field yields k[\(\Delta]\) being Gorenstein over any field. The given triangulation of \(P^ 3\) is false; it even fails to satisfy the generalized Dehn-Sommerville equations.
Mathematics Subject Classification ID: 13H10
Mathematics Subject Classification ID: 13D25
Mathematics Subject Classification ID: 14M05
Mathematics Subject Classification ID: 13F20
zbMATH DE Number: 3875430
zbMATH Keywords: Gorenstein property
zbMATH Keywords: Stanley-Reisner rings
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3875430