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FINITE CONJUGACY IN ALGEBRAS AND ORDERS

Published online by Cambridge University Press:  20 January 2009

M. A. Dokuchaev ,
S. O. Juriaans ,
C. Polcino Milies  and
M. L. Sobral Singer
M. A. Dokuchaev
Affiliation:
Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66281, 05315-970 São Paulo, BR (dokucha@ime.usp.br; ostanley@ime.usp.br; polcino@ime.usp.br; mlucia@ime.usp.br)
S. O. Juriaans
Affiliation:
Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66281, 05315-970 São Paulo, BR (dokucha@ime.usp.br; ostanley@ime.usp.br; polcino@ime.usp.br; mlucia@ime.usp.br)
C. Polcino Milies
Affiliation:
Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66281, 05315-970 São Paulo, BR (dokucha@ime.usp.br; ostanley@ime.usp.br; polcino@ime.usp.br; mlucia@ime.usp.br)
M. L. Sobral Singer
Affiliation:
Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66281, 05315-970 São Paulo, BR (dokucha@ime.usp.br; ostanley@ime.usp.br; polcino@ime.usp.br; mlucia@ime.usp.br)
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Abstract

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Herstein showed that the conjugacy class of a non-central element in the multiplicative group of a division ring is infinite. We prove similar results for units in algebras and orders and give applications to group rings.

AMS 2000 Mathematics subject classification: Primary 16U60. Secondary 16H05; 16S34; 20F24; 20C05

Keywords

algebrasordersunitsfinite conjugacy
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 44 , Issue 1 , February 2001 , pp. 201 - 213
Copyright
Copyright © Edinburgh Mathematical Society 2001