Verbal subgroups and subalgebras in skew fields.
type: Item
instance of: scholarly article
title: Verbal subgroups and subalgebras in skew fields.
zbMATH Open document ID: 1090.16006
author: A. I. Lichtman
published in: Algebras and Representation Theory
publication date: 2006-02-23T00:00:00Z
review text: Let \(D\) be an arbitrary skew field with central subfield \(K\). The author shows that \(D\) can be embedded in a skew field \(\Delta\) such that \(w(\Delta)=\Delta\) for any nonempty Lie word \(w\) on a set of variables \(y_1,y_2,\dots\) with coefficients in \(K\). Furthermore, for every nonempty word \(v=x_1^{\epsilon_1}x_2^{\epsilon_2}\cdots x_n^{\epsilon_n}\) with \(\epsilon_1,\dots,\epsilon_n\in\{-1,1\}\), the multiplicative group \(\Delta^*\) is such that \(w(\Delta^*)=\Delta^*\).
reviewed by: Hai Quang Dinh
Mathematics Subject Classification ID: 16K40
Mathematics Subject Classification ID: 16S10
Mathematics Subject Classification ID: 16U60
zbMATH DE Number: 5009032
zbMATH Keywords: skew fields
zbMATH Keywords: free algebras
zbMATH Keywords: Lie polynomials
zbMATH Keywords: embeddings
zbMATH Keywords: group words
zbMATH Keywords: Lie words
zbMATH Keywords: multiplicative groups
MaRDI profile type: Publication
full work available at URL: s10468-005-3570-y
OpenAlex ID: W2066932579
cites work: Q3503673
cites work: Cohomological topics in group theory.
cites work: Commutators in Division Rings
cites work: An embedding of the group algebra of a torsion-free one-relator group in a field
cites work: An example of a skew field without a trace
cites work: Q5507609
DOI: 10.1007/S10468-005-3570-Y
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description: scientific article; zbMATH DE number 5009032