Free products arising from elements of finite order in simple rings
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- by M. Shirvani and J. Z. Gonçalves PDF
- Proc. Amer. Math. Soc. 133 (2005), 1917-1923 Request permission
Abstract:
Our main result implies that, if $R$ is a simple artinian ring which is not a matrix ring over an absolute field, then any noncentral element of $R$, of prime order not dividing the characteristic, is a factor in a free product with a unit which has infinite order in $R$. Unexpected consequences follow for division rings and group algebras.References
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Additional Information
- M. Shirvani
- Affiliation: Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1
- Email: mshirvan@ualberta.ca
- J. Z. Gonçalves
- Affiliation: Departamento de Matemática, Universidade de São Paulo, São Paulo, SP Brazil 05508-970
- MR Author ID: 75040
- Email: jzg@ime.usp.br
- Received by editor(s): April 6, 2003
- Received by editor(s) in revised form: March 2, 2004
- Published electronically: January 21, 2005
- Additional Notes: The research of the first author was partially supported by NSERC, Canada, and Fapesp (Projeto Temático 00/07.291-0).
The research of the second author was partially supported by CNPq-Brazil (Grant 302.756/82-5) and Fapesp (Projeto Temático 00/07.291-0). - Communicated by: Martin Lorenz
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 133 (2005), 1917-1923
- MSC (2000): Primary 16S36; Secondary 16K40, 16P90
- DOI: https://doi.org/10.1090/S0002-9939-05-07764-6
- MathSciNet review: 2137855