Exponent reduction for radical Abelian algebras
type: Item
instance of: scholarly article
title: Exponent reduction for radical Abelian algebras
zbMATH Open document ID: 0955.16022
author: Eli Aljadeff
author: Jack Sonn
published in: Journal of Algebra
publication date: 2000-06-22T00:00:00Z
review text: Let \(A\) be a radical Abelian algebra over a field \(k\), i.e., \(A\) is a crossed product \((K/k,G,\alpha)\) where \(K=k(T)\) is a radical Abelian extension of \(k\), \(T\) is a subgroup of \(K^*\) which is finite modulo \(k^*\) and \(\alpha\in H^2(G,K^*)\) is represented by a cocyle with values in \(T\). Let also \(\mu\) be the group of all roots of unity in an algebraic closure of \(k\). The authors prove that \(K\) contains a primitive root of unity of order \(\exp(A\otimes_k k(\mu))\).
Mathematics Subject Classification ID: 16K50
Mathematics Subject Classification ID: 16S35
Mathematics Subject Classification ID: 16K20
zbMATH DE Number: 1423883
zbMATH Keywords: radical Abelian algebras
zbMATH Keywords: crossed products
zbMATH Keywords: radical Abelian extensions
reviewed by: Yu. N. Maltsev
MaRDI profile type: Publication
full work available at URL: jabr.1999.8057
OpenAlex ID: W1987136646
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DOI: 10.1006/JABR.1999.8057
description: scientific article; zbMATH DE number 1423883