On the isomorphic classes of Hopf-Galois extensions with normal bases over a commutative ring
type: Item
instance of: scholarly article
title: On the isomorphic classes of Hopf-Galois extensions with normal bases over a commutative ring
zbMATH Open document ID: 0942.16042
author: Xiao-Long Jiang
author: Xu Yonghua
publication date: 2000-06-04T00:00:00Z
review text: Let \(H\) be a finite cocommutative Hopf algebra over a commutative ring. The authors show that the isomorphism types of \(H\)-Galois extensions with the normal basis property of a fixed commutative ring \(B\) are in bijection with the cohomology group \(H^2(L^*,U)\), where \(L=B\otimes H\) and \(L^*=\text{Hom}_B(L,B)\). Related work has been done by \textit{Y. Doi} [Commun. Algebra 17, No. 12, 3053-3085 (1989; Zbl 0687.16008)].
Mathematics Subject Classification ID: 16W30
zbMATH DE Number: 1385068
zbMATH Keywords: Hopf algebras
zbMATH Keywords: Hopf-Galois extensions
zbMATH Keywords: normal basis property
zbMATH Keywords: smash products
reviewed by: Sorin Dascalescu
MaRDI profile type: Publication
full work available at URL: s10114-999-0083-3
OpenAlex ID: W2081709266
cites work: Q3897166
cites work: Hopf-Galois extensions of algebras, the Miyashita-Ulbrich action, and Azumaya algebras
cites work: Hopf algebras and Galois theory
cites work: Separable algebras over commutative rings
cites work: Galois-type correspondences for Hopf-Galois extensions
cites work: Principal homogeneous spaces for arbitrary Hopf algebras
cites work: The Predual Theorem to the Jacobson-Bourbaki Theorem
cites work: Q4075558
cites work: Non-commutative Hopf Galois extensions
cites work: The cohomological aspects of Hopf Galois extensions over a commutative ring
DOI: 10.1007/S10114-999-0083-3
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 1385068