Linkage of finite Gorenstein dimension modules
type: Item
instance of: scholarly article
title: Linkage of finite Gorenstein dimension modules
zbMATH Open document ID: 1282.13024
author: Mohammad T. Dibaei
author: Arash Sadeghi
published in: Journal of Algebra
publication date: 2013-08-26T00:00:00Z
full work available at URL: https://arxiv.org/abs/1109.6528
full work available at URL: S0021869312006011
review text: The modern theory of linkage for subschemes of projective space was introduced by C. Peskine and L. Szpiro in 1974, although its origins go back much farther. A great deal of work in the setting of ideals in a local ring was done most notably by C. Huneke and B. Ulrich in the 1980's. A few authors advanced the theory to the setting of linkage of modules in the 2000's, for instance U. Nagel, H. Martin, A. Martsinkovsky and J.R. Strooker, and Y. Yoshino and S. Isogawa. In particular, Martsinkovsky and Strooker define the notion of \textit{horizontal linkage} for modules. In this paper the authors study the theory of linkage for a class of modules which have finite Gorenstein dimension. For a horizontally linked module \(M\) over a commutative semiperfect Noetherian ring \(R\), they study the connections of its reduced grade, its Gorenstein dimension, and its depth. They also discuss the connection between the Serre condition \((S_n)\) on an \(R\)-module of finite Gorenstein dimension and the vanishing of the local cohomology groups of its linked module.
reviewed by: Juan C. Migliore
Mathematics Subject Classification ID: 13C40
Mathematics Subject Classification ID: 13D45
zbMATH DE Number: 6201466
zbMATH Keywords: linkage of modules
zbMATH Keywords: Gorenstein dimension
zbMATH Keywords: reduced grade
zbMATH Keywords: semidualizing module
zbMATH Keywords: \(G_K\)-dimension
MaRDI profile type: Publication
OpenAlex ID: W2005263246
arXiv ID: 1109.6528
DOI: 10.1016/J.JALGEBRA.2012.11.035
description: scientific article; zbMATH DE number 6201466