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)



Trace methods in twisted group algebras

Author: D. S. Passman
Journal: Proc. Amer. Math. Soc. 129 (2001), 943-946
MSC (2000): Primary 16S35
Published electronically: October 16, 2000
MathSciNet review: 1707017
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this brief note, we discuss trace methods in twisted group algebras. Specifically, we obtain information on the trace of idempotent and nilpotent elements. As is to be expected, if the ground field has positive characteristic, then the arguments used for ordinary group rings carry over to this context with little difficulty. On the other hand, lifting these results to characteristic zero algebras is not straightforward and requires a reduction to finitely presented groups.

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

  • [K] I. Kaplansky, Fields and Rings, Chicago Lectures in Math., Univ. of Chicago Press, Chicago, 1969. MR 42:4345
  • [P1] D. S. Passman, Radicals of twisted group rings, Proc. London Math. Soc. (3) 20 (1970), 409-437. MR 42:6129
  • [P2] -, The Algebraic Structure of Group Rings, Wiley-Interscience, New York, 1977. MR 81d:16001
  • [Z] A. E. Zalesskii, On a problem of Kaplansky, Soviet Math. 13 (1972), 449-452. MR 45:6947

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 16S35

Retrieve articles in all journals with MSC (2000): 16S35

Additional Information

D. S. Passman
Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706

Received by editor(s): June 14, 1999
Published electronically: October 16, 2000
Additional Notes: This research was supported by NSF Grant DMS-9820271. The author would like to thank Prof. Jairo Z. Gonçalves for interesting conversations on this subject.
Communicated by: Lance W. Small
Article copyright: © Copyright 2000 American Mathematical Society

American Mathematical Society