On characterizations of a center Galois extension
type: Item
instance of: scholarly article
title: On characterizations of a center Galois extension
zbMATH Open document ID: 1003.16016
DOI: 10.1155/S0161171200003562
author: George Szeto
author: Lianyong Xue
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2002-10-28T00:00:00Z
full work available at URL: https://eudml.org/doc/49667
review text: Let \(B\) be a ring with identity, \(C\) the center of \(B\), \(G\) a finite automorphism group of \(B\) and \(B^G\) the set of elements in \(B\) fixed under each element in \(G\). The main result established by the authors is: \(B\) is a center Galois extension of \(B^G\) (that is, \(C\) is a Galois algebra over \(C^G\) with Galois group \(G|_C\cong G\)) if and only if the ideal of \(B\) generated by \(\{c-g(c)\mid c\in C\}\) is \(B\) for each \(g\neq 1\) in \(G\).
reviewed by: Iuliu Crivei
Mathematics Subject Classification ID: 16S35
Mathematics Subject Classification ID: 16W22
Mathematics Subject Classification ID: 16W20
Mathematics Subject Classification ID: 16H05
zbMATH DE Number: 1501976
zbMATH Keywords: center Galois extensions
zbMATH Keywords: finite automorphism groups
zbMATH Keywords: Galois groups
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1501976