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

 

Free products arising from elements of finite order in simple rings


Authors: M. Shirvani and J. Z. Gonçalves
Journal: Proc. Amer. Math. Soc. 133 (2005), 1917-1923
MSC (2000): Primary 16S36; Secondary 16K40, 16P90
Published electronically: January 21, 2005
MathSciNet review: 2137855
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Abstract | References | Similar Articles | Additional Information

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.


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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
Email: jzg@ime.usp.br

DOI: http://dx.doi.org/10.1090/S0002-9939-05-07764-6
PII: S 0002-9939(05)07764-6
Keywords: Simple ring, division ring, element of finite order, free product over the center
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
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.