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On free group algebras in division rings with uncountable center
Author(s):
J.
Goncalves;
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  be a division algebra with uncountable center  . If  contains a noncommutative free  -algebra, then  also contains the  -group algebra of the free group of rank 2.
References:
- 1.
- J. Z. Goncalves and M. Shirvani, On free subalgebras in division algebras and related rings, preprint.
- 2.
- A. I. Lichtman, On subgroups of the multiplicative group of skew fields, Proc. Amer. Math. Soc. 63 (1977), 15--16. MR 56:5744
- 3.
- ------, Free subgroups of normal subgroups of the multiplicative group of skew fields, Proc. Amer. Math. Soc. 71 (1978), 174--178. MR 58:779
- 4.
- ------, On normal subgroups of the multiplicative group of skew fields generated by a polycyclic-by-finite group, J. Algebra 78 (1982), 548--577. MR 84f:16016
- 5.
- M. Lorenz, On free subalgebras of certain division algebras, Proc. Amer. Math. Soc. 98 (1986), 401--405. MR 87m:16040
- 6.
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- 7.
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- 8.
- ------, On group rings of nilpotent groups, Israel J. Math. 48 (1984), 245--248. MR 86c:16006
- 9.
- L. Makar-Limanov and P. Malcolmson, Words periodic over the center of a division ring, Proc. Amer. Math. Soc. 93 (1985), 590--592. MR 86g:16026
- 10.
- L. Makar-Limanov, On subnormal subgroups of skew fields, J. Algebra 114 (1988), 261--267. MR 89d:16024
- 11.
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- 12.
- L. Makar-Limanov and P. Malcolmson, Free subalgebras of enveloping algebras, Proc. Amer. Math. Soc. 11 (1991), 315--322. MR 91f:16023
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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:
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
Copyright of article:
Copyright
1996,
American Mathematical Society
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