Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9939-05-07764-6
Published electronically: January 21, 2005
MathSciNet review: 2137855
Full-text PDF

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.


References [Enhancements On Off] (What's this?)

  • 1. P. M. Cohn, Algebra, Wiley and Sons, London, 1977. MR 0530404 (58:26625)
  • 2. J. Z. Gonçalves, A. Mandel, and M. Shirvani, Free Products of Units. II. J. Algebra 233, 567-593 (2000). MR 1793917 (2002c:16044)
  • 3. J. Z. Gonçalves, and D. S. Passman, Embedding free products in the unit group of an integral group ring, Archiv der Mathematik, (Basel) 82, 97-102 (2004). MR 2047662
  • 4. P. Gorbounov, M. Mahowald, and P. Symonds, Infinite subgroups of the Morava stabilizer groups, Topology 37(6), 1371-1379 (1998). MR 1632952 (99m:16032)
  • 5. I. N. Herstein, Noncommutative Rings, Mathematical Association of America, (1968). MR 0227205 (37:2790)
  • 6. I. N. Herstein, Multiplicative commutators in division rings, II. Rend. Circ. Mat. Palermo 29(3), 485-489 (1980). MR 0638685 (83a:16043)
  • 7. I. Kaplansky, Fields and Rings, University of Chicago Press, (1969). MR 0269449 (42:4345)
  • 8. T. Y. Lam, A First Course in Non-commutative Ring Theory, Springer Verlag, New York, (1991). MR 1125071 (92f:16001)
  • 9. L. H. Rowen, Ring Theory I, Academic Press, (1988). MR 0940245 (89h:16001)
  • 10. B. A. F. Wehrfritz, Infinite Linear Groups, Springer Verlag, New York, (1973). MR 0335656 (49:436)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 16S36, 16K40, 16P90

Retrieve articles in all journals with MSC (2000): 16S36, 16K40, 16P90


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.

American Mathematical Society