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On free subgroups of units of rings


Author: A. Salwa
Journal: Proc. Amer. Math. Soc. 127 (1999), 2569-2572
MSC (1991): Primary 16U60
DOI: https://doi.org/10.1090/S0002-9939-99-05309-5
Published electronically: May 17, 1999
MathSciNet review: 1662206
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Abstract: We prove that if $a^{2}=b^{2}=0$ for elements $a,b$ of a ring $R$ of characteristic zero and $ab$ is not nilpotent, then there exists $m\in {\mathbf N}$ such that the group generated by $1+ma$ and $1+mb$ is free nonabelian. This is used to prove that a noncommutative positive-definite algebra with involution over an uncountable field contains a free nonabelian subsemigroup.


References [Enhancements On Off] (What's this?)

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Additional Information

A. Salwa
Email: asalwa@mimuw.edu.pl

DOI: https://doi.org/10.1090/S0002-9939-99-05309-5
Received by editor(s): October 15, 1997
Published electronically: May 17, 1999
Additional Notes: The author was supported by KBN reasearch grant 2P03A 003 12.
Communicated by: Ronald M. Solomon
Article copyright: © Copyright 1999 American Mathematical Society

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