Semi-dualizing modules and related Gorenstein homological dimensions
type: Item
instance of: scholarly article
title: Semi-dualizing modules and related Gorenstein homological dimensions
zbMATH Open document ID: 1094.13021
author: Henrik Holm
author: Peter Jørgensen
published in: Journal of Pure and Applied Algebra
publication date: 2006-03-29T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/0405526
review text: In this paper, the authors define for every semi-dualizing \(A\)-module \(C\), three new Gorenstein dimensions: \(C-\text{Gid}_A(-)\), \(C-\text{Gpd}_A(-)\) and \(C-\text{Gfd}_A(-)\), which are called the \(C\)-Gorenstein injective, \(C\)-Gorenstein projective and \(C\)-Gorenstein flat dimension, respectively, and prove how they are related to the ``change ring'' Gorenstein dimensions over \(A\ltimes C\). Moreover, the authors interpret the \(C\)-Gorenstein dimensions in terms of Auslander and Bass categories and investigate the properties of proper \(C\)-Gorenstein dimensions.
reviewed by: Jianming Zhan
Mathematics Subject Classification ID: 13D05
Mathematics Subject Classification ID: 13D07
Mathematics Subject Classification ID: 13D25
Mathematics Subject Classification ID: 18G10
Mathematics Subject Classification ID: 18G25
zbMATH DE Number: 5016253
MaRDI profile type: Publication
OpenAlex ID: W1997645797
arXiv ID: math/0405526
cites work: Gorenstein dimensions
cites work: Semi-dualizing complexes and their Auslander categories. -- Appendix: Chain defects
cites work: On Gorenstein projective, injective and flat dimensions -- a functorial description with applications
cites work: Gorenstein injective and projective modules
cites work: Relative homological algebra
cites work: \(\lambda\) and \(\mu\)-dimensions of modules.
cites work: Kaplansky classes
cites work: Residues and duality. Lecture notes of a seminar on the work of A. Grothendieck, given at Havard 1963/64. Appendix: Cohomology with supports and the construction of the \(f^!\) functor by P. Deligne
cites work: Gorenstein homological dimensions.
cites work: Rings with finite Gorenstein injective dimension
cites work: Gorenstein projective dimension for complexes
cites work: Q4296949
cites work: Flat covers of modules
DOI: 10.1016/J.JPAA.2005.07.010
description: scientific article