On central commutator Galois extensions of rings
type: Item
instance of: scholarly article
title: On central commutator Galois extensions of rings
zbMATH Open document ID: 1003.16018
DOI: 10.1155/S0161171200004099
author: George Szeto
author: Lianyong Xue
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2002-10-29T00:00:00Z
full work available at URL: https://eudml.org/doc/49668
review text: Let \(B\) be a ring with identity, \(G\) a finite automorphism group of \(B\) of order \(n\) for some integer \(n\), \(B^G\) the set of elements in \(B\) fixed under each element in \(G\), and \(\Delta=V_B(B^G)\) the commutator subring of \(B^G\) in \(B\). Let \(A\) be a subring of \(B\). The ring \(B\) is called an \(H\)-separable extension of \(A\) if \(B\times_AB\) is isomorphic to a direct summand of a finite direct sum of \(B\) as a \(B\)-bimodule. \(B\) is called a central commutator Galois extension of \(B^G\) if \(\Delta\) is a central Galois algebra with Galois group \(G|_C\cong G\). The authors give several characterizations of a central commutator Galois extension. Also, the authors show that when \(G\) is inner, \(B\) is a central commutator Galois extension of \(B^G\) if and only if \(B\) is an \(H\)-separable projective group ring \(B^GG_f\).
reviewed by: Iuliu Crivei
Mathematics Subject Classification ID: 16S35
Mathematics Subject Classification ID: 16W22
Mathematics Subject Classification ID: 16H05
Mathematics Subject Classification ID: 16W20
zbMATH DE Number: 1533308
zbMATH Keywords: central commutator Galois extensions
zbMATH Keywords: separable extensions
zbMATH Keywords: finite automorphism groups
zbMATH Keywords: direct sums
zbMATH Keywords: bimodules
zbMATH Keywords: Galois algebras
zbMATH Keywords: Galois groups
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description: scientific article; zbMATH DE number 1533308