Embedding division algebras in crossed products
type: Item
instance of: scholarly article
title: Embedding division algebras in crossed products
zbMATH Open document ID: 0862.16010
author: Burton Fein
author: David Saltman
author: Murray M. Schacher
published in: Journal of Algebra
publication date: 1997-05-26T00:00:00Z
review text: Let \(D\) be a division algebra having center \(F\) which is finite dimensional over \(F\). If there exists a maximal subfield \(E\) of \(D\) which is Galois over \(F\), \(D\) is called a crossed product (or \(G\)-crossed product if \(G=\text{Gal}(E/F)\)). If no such \(E\) exists, \(D\) is called a noncrossed product. Let \(UD(F,n,r)\) be the generic division algebra of degree \(n>1\) generated by \(r\) \((n,n)\) generic matrices over \(F\). They are noncrossed product by S. Amitsur (1972). But ``most'' of them embedd into crossed products. Theorem 3. Let \(F\) be a field, \(n>1\). There exists an integer \(R\) such that if \(r>R\), then \(UD(F,n,r)\) centrally embeds in an \(S(n)\)-crossed product division algebra.
Mathematics Subject Classification ID: 16K20
Mathematics Subject Classification ID: 16S35
zbMATH DE Number: 922321
zbMATH Keywords: generic division algebras
zbMATH Keywords: crossed products
reviewed by: Leonid A. Bokut'
MaRDI profile type: Publication
full work available at URL: jabr.1996.0187
OpenAlex ID: W2084953740
DOI: 10.1006/JABR.1996.0187
description: scientific article; zbMATH DE number 922321