On free subgroups of units of rings
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- by A. Salwa PDF
- Proc. Amer. Math. Soc. 127 (1999), 2569-2572 Request permission
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
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Additional Information
- A. Salwa
- Email: asalwa@mimuw.edu.pl
- 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
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 2569-2572
- MSC (1991): Primary 16U60
- DOI: https://doi.org/10.1090/S0002-9939-99-05309-5
- MathSciNet review: 1662206