\(\mathbb{W}^t\)-approximation representations over quasi \(k\)-Gorenstein algebras
type: Item
instance of: scholarly article
title: \(\mathbb{W}^t\)-approximation representations over quasi \(k\)-Gorenstein algebras
zbMATH Open document ID: 0966.16004
DOI: 10.1007/BF02880386
published in: Science in China. Series A
publication date: 2000-08-28T00:00:00Z
review text: For any positive integer \(k\) Auslander introduced the notion of \(k\)-Gorenstein algebra in the non-commutative case and proved that the \(k\)-Gorenstein algebras are left-right symmetric. Then \textit{M. Auslander} and \textit{I. Reiten} studied the homological finiteness of categories of modules over \(k\)-Gorenstein algebras [see J. Pure Appl. Algebra 92, No. 1, 1-27 (1992; Zbl 0803.16016)]. In the paper under review the author introduces first the notion of quasi \(k\)-Gorenstein algebra and shows by examples that this notion deserves to be studied (in particular, unlike in the \(k\)-Gorenstein case, the quasi \(k\)-Gorenstein algebras are not always left-right symmetric). Then, in connection with a series of papers by M. Auslander and I. Reiten on the representation theory of Artin algebras, he defines and studies the notion of \(\mathbb{W}^t\)-approximation representation. Some applications to homologically finite subcategories are given. This paper is based on a part of the author's Ph.D. thesis.
Mathematics Subject Classification ID: 16E65
Mathematics Subject Classification ID: 16G70
Mathematics Subject Classification ID: 16G30
Mathematics Subject Classification ID: 16D90
zbMATH DE Number: 1439324
zbMATH Keywords: Gorenstein algebras
zbMATH Keywords: quasi Gorenstein algebras
zbMATH Keywords: approximation representations
zbMATH Keywords: categories of modules
zbMATH Keywords: homologically finite categories
author: Zhaoyong Huang
reviewed by: Lucian Bădescu
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02880386
OpenAlex ID: W2764684377
description: scientific article; zbMATH DE number 1439324