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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On free group algebras in division rings
with uncountable center


Authors: J. Goncalves and M. Shirvani
Journal: Proc. Amer. Math. Soc. 124 (1996), 685-687
MSC (1991): Primary 16A39; Secondary 16A06, 16A48
MathSciNet review: 1291771
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Abstract: Let $D$ be a division algebra with uncountable center $k$. If $D$ contains a noncommutative free $k$-algebra, then $D$ also contains the $k$-group algebra of the free group of rank 2.


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Additional Information

J. Goncalves
Affiliation: Department of Mathematics, University of Sao Paulo, CP 66281, 05389-970 Sao Paulo SP, Brazil
Email: jzg@ime.usp.br

M. Shirvani
Affiliation: Department of Mathematics, University of Alberta, Edmonton, Alberta, Canada T6G 2G1
Email: mazi@schur.math.ualberta.ca

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03032-8
PII: S 0002-9939(96)03032-8
Keywords: Division ring, free algebra, free group algebra
Received by editor(s): September 21, 1993
Received by editor(s) in revised form: July 25, 1994
Communicated by: Ken Goodearl
Article copyright: © Copyright 1996 American Mathematical Society