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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Free algebras and free groups in Ore extensions and free group algebras in division rings

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Author(s):
Bell, Jason P. [1] ; Goncalves, Jairo Z. [2]
Total Authors: 2
Affiliation:
[1] Univ Waterloo, Dept Pure Math, Waterloo, ON N2L 3G1 - Canada
[2] Univ Sao Paulo, Dept Math, BR-05508090 Sao Paulo - Brazil
Total Affiliations: 2
Document type: Journal article
Source: Journal of Algebra; v. 455, p. 235-250, JUN 1 2016.
Web of Science Citations: 2
Abstract

Let K be a field of characteristic zero, let sigma be an automorphism of K and let delta be a sigma-derivation of K. We show that the division ring D = K(x; sigma, delta) either has the property that every finitely generated subring satisfies a polynomial identity or D contains a free algebra on two generators over Its center. In the case when K is finitely generated over a subfield k we then see that for sigma a k-algebra automorphism of K and delta a k-linear derivation of K, K(x; sigma) having a free subalgebra on two generators is equivalent to sigma having infinite order, and K(x; delta) having a free subalgebra is equivalent to delta being nonzero. As an application, we show that if D is a division ring with center k of characteristic zero and D{*} contains a solvable subgroup that is not locally abelian-by-finite, then D contains a free k-algebra on two generators. Moreover, if we assume that k is uncountable, without any restrictions on the characteristic of k, then D contains the k-group algebra of the free group of rank two. (C) 2016 Elsevier Inc. All rights reserved. (AU)

FAPESP's process: 09/52665-0 - Groups, rings and algebras: interactions and applications
Grantee:Francisco Cesar Polcino Milies
Support type: Research Projects - Thematic Grants