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 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:
https://doi.org/10.1090/S0002-9939-05-07764-6

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.