On the existence of Gorenstein projective precovers
type: Item
instance of: scholarly article
title: On the existence of Gorenstein projective precovers
zbMATH Open document ID: 1356.16002
DOI: 10.4171/RSMUP/136-16
author: Javad Asadollahi
author: Tahereh Dehghanpour
author: Rasool Hafezi
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 2017-02-15T00:00:00Z
review text: Summary: We provide a simple proof for a recent result of \textit{D. Bravo}, \textit{J. Gillespie} and \textit{M. Hovey} [``The stable module category of a general ring'', Preprint, \url{arXiv:1405.5768v1}], showing that over a left coherent ring for which the projective dimension of at right modules is finite, the class of Gorenstein projective right modules is precovering. As an immediate application, we provide a description for the Gorenstein defect category over such rings.
Mathematics Subject Classification ID: 16D40
Mathematics Subject Classification ID: 16D90
Mathematics Subject Classification ID: 16E65
zbMATH DE Number: 6684908
zbMATH Keywords: precovering class
zbMATH Keywords: Gorenstein projective
zbMATH Keywords: Gorenstein flat
MaRDI profile type: Publication
cites work: Homotopy category of projective complexes and complexes of Gorenstein projective modules.
cites work: Cohen-Macaulay modules, (co)torsion pairs and virtually Gorenstein algebras.
cites work: On algebras of finite Cohen-Macaulay type.
cites work: THE GORENSTEIN DEFECT CATEGORY
cites work: ALL MODULES HAVE FLAT COVERS
cites work: Gorenstein complexes and recollements from cotorsion pairs
cites work: Gorenstein homological dimensions.
cites work: The homotopy category of complexes of projective modules
cites work: From CM-finite to CM-free
cites work: Totally acyclic complexes over noetherian schemes
cites work: All Modules Have Gorenstein Flat Precovers
description: scientific article; zbMATH DE number 6684908