Equivalence theorems and Hopf-Galois extensions
type: Item
instance of: scholarly article
title: Equivalence theorems and Hopf-Galois extensions
zbMATH Open document ID: 0884.16024
author: Monica Zuccoli
author: Claudia Menini
published in: Journal of Algebra
publication date: 1998-02-02T00:00:00Z
review text: This work studies equivalence theorems for categories \({\mathcal M}(H)^D_A\) of right (\(D\)-\(A\))-Hopf modules. The authors get a characterization of the Hopf-Galois extensions. The paper has three main parts. In section two the notions which are going to be used are defined and some of the theorems relating the category of modules over a ring and the category of modules over its endomorphism ring are proved. Some of the results in this section are not new, but their inclusion in the paper makes it much more readable. When \(P\) is an \(R\) module and \(T=\text{End}(P)\) then the functors \(\text{Hom}_R(P,-)\) and \(-\otimes_TP\) are studied, in particular in the case where \(P\) is a quasiprogenerator. In the third section appear the main results which are obtained as applications of the theorems in section 2 to the case of an \(H\)-comodule algebra and \(H\)-module algebra. In the last section there are some applications to the finite dimensional case. The paper is almost self contained, which does not mean easy. The results of section 2, which make the work selfcontained, stand for themselves, and could have various other applications.
Mathematics Subject Classification ID: 16W30
Mathematics Subject Classification ID: 16D90
Mathematics Subject Classification ID: 16D80
Mathematics Subject Classification ID: 16D40
zbMATH DE Number: 1053883
zbMATH Keywords: progenerators
zbMATH Keywords: comodule algebras
zbMATH Keywords: categories of Hopf modules
zbMATH Keywords: equivalences of categories
zbMATH Keywords: endomorphism rings
zbMATH Keywords: Hopf-Galois extensions
reviewed by: Eduardo N. Marcos
MaRDI profile type: Publication
full work available at URL: jabr.1996.6994
OpenAlex ID: W2083100846
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DOI: 10.1006/JABR.1996.6994
description: scientific article; zbMATH DE number 1053883