Gorenstein injective and projective modules and actions of finite-dimensional Hopf algebras.
type: Item
instance of: scholarly article
title: Gorenstein injective and projective modules and actions of finite-dimensional Hopf algebras.
zbMATH Open document ID: 1159.16030
author: J. A. López-Ramos
published in: Arkiv för Matematik
publication date: 2008-10-27T00:00:00Z
review text: Let \(H\) be a finite dimensional Hopf algebra over a field \(k\), let \(A\) be a left \(H\)-module algebra and \(B=A^{co\,H}\) the algebra of coinvariants. In this paper, the author considers the problem of preserving properties of covers between the categories of modules over \(A\), \(B\) and the smash product \(A\#H\). These results extend the graded case by \textit{M. J. Asensio}, the author and the reviewer [J. Algebra 215, No. 2, 437-459 (1999; Zbl 0942.16049)]. In the last section, as consequence of the previous results, new examples of Gorenstein categories, as defined by \textit{E. Enochs, S. Estrada} and \textit{J. R. García-Rozas} [in Math. Nachr. 281, No. 4, 525-540 (2008; Zbl 1146.18004)], are presented.
reviewed by: Blas Torrecillas
Mathematics Subject Classification ID: 16W30
Mathematics Subject Classification ID: 16E65
Mathematics Subject Classification ID: 16D40
Mathematics Subject Classification ID: 16D50
Mathematics Subject Classification ID: 16E10
zbMATH DE Number: 5357909
zbMATH Keywords: Gorenstein injective modules
zbMATH Keywords: Hopf extensions
zbMATH Keywords: Gorenstein categories
zbMATH Keywords: preenvelopes
zbMATH Keywords: precovers
zbMATH Keywords: smash products
zbMATH Keywords: Gorenstein dimensions
MaRDI profile type: Publication
full work available at URL: s11512-007-0053-x
OpenAlex ID: W2087553982
Wikidata QID: Q114222268
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DOI: 10.1007/S11512-007-0053-X
description: scientific article; zbMATH DE number 5357909