\(\mathcal{W}\)-Gorenstein \(N\)-complexes
type: Item
instance of: scholarly article
title: \(\mathcal{W}\)-Gorenstein \(N\)-complexes
zbMATH Open document ID: 1437.18008
DOI: 10.1216/RMJ-2019-49-6-1973
author: Bo Lü
author: Jiaqun Wei
author: Zhenxing Di
published in: Rocky Mountain Journal of Mathematics
publication date: 2019-11-26T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.rmjm/1572746429
review text: Let \(\mathcal{A}\) be an abelian category with enough projectives and injectives, and let \(\mathcal{W}\) be a self-orthogonal subcategory of \(\mathcal{A}\) in the sense of \textit{S. Sather-Wagstaff} et al. [J. Lond. Math. Soc., II. Ser. 77, No. 2, 481--502 (2008; Zbl 1140.18010)]. The main result of the paper says that if \(G\) is an \(N\)-complex in \(\mathcal{A}\) (where \(N\geq 2\)), then \(G\) is a \(\mathcal{W}\)-Gorenstein \(N\)-complex if and only if \(G\) consists of \(\mathcal{W}\)-Gorenstein objects in \(\mathcal{A}\). As an application it is obtained that if \(R\) is a ring, then an \(N\)-complex of \(R\)-modules is Gorenstein injective if and only if it consists of Gorenstein injective modules.
reviewed by: Constantin Năstăsescu
Mathematics Subject Classification ID: 18G25
Mathematics Subject Classification ID: 18G35
Mathematics Subject Classification ID: 18E10
zbMATH DE Number: 7136589
zbMATH Keywords: \(\mathcal{W}\,N\)-complex
zbMATH Keywords: \(\mathcal{W}\)-Gorenstein \(N\)-complex
zbMATH Keywords: \(\mathcal{W}\)-Gorenstein object
zbMATH Keywords: Gorenstein injective \(N\)-complex
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 7136589