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Communications in Algebra Volume 40, 2012 - Issue 5
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Original Articles

A Survey on Free Objects in Division Rings and in Division Rings with an Involution

J. Z. Gonçalves Department of Mathematics, University of São Paulo, São Paulo, BrazilCorrespondence[email protected]
&
M. Shirvani Department of Mathematics and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada
Pages 1704-1723 | Received 24 Oct 2010, Published online: 15 May 2012
 
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Abstract

Let D be a division ring with center k, and let D † be its multiplicative group. We investigate the existence of free groups in D †, and free algebras and free group algebras in D. We also go through the case when D has an involution * and consider the existence of free symmetric and unitary pairs in D †.

ACKNOWLEDGMENT

The first author's research was partially supported by Grant CNPq 300.128/2008-8, and Fapesp-Brazil, Proj. Tematico 2009/52665-0.

Notes

Communicated by S. Sehgal.

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