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Free products arising from elements of finite order in simple rings
Author(s):
M.
Shirvani;
J.
Z.
Gonçalves
Journal:
Proc. Amer. Math. Soc.
133
(2005),
1917-1923.
MSC (2000):
Primary 16S36;
Secondary 16K40, 16P90
Posted:
January 21, 2005
MathSciNet review:
2137855
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Abstract:
Our main result implies that, if  is a simple artinian ring which is not a matrix ring over an absolute field, then any noncentral element of  , of prime order not dividing the characteristic, is a factor in a free product with a unit which has infinite order in  . 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:
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
Posted:
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 of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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