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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Wang counterexamples lead
to noncrossed products


Author: Eric S. Brussel
Journal: Proc. Amer. Math. Soc. 125 (1997), 2199-2206
MSC (1991): Primary 16S35; Secondary 11R37
MathSciNet review: 1371116
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Abstract: Two famous counterexamples in algebra and number theory are Wang's counterexample to Grunwald's Theorem and Amitsur's noncrossed product division algebra. In this paper we use Wang's counterexample to construct a noncrossed product division algebra.

In the 30's, Grunwald's Theorem was used in the proof of a major result of class field theory, that all division algebras over number fields are (cyclic) crossed products. It is ironic that now Grunwald-Wang's Theorem is the decisive factor in a noncrossed product construction.


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Additional Information

Eric S. Brussel
Affiliation: Department of Mathematics, Harvard University, Cambridge, Massachusetts 02143
Email: brussel@math.harvard.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03725-8
PII: S 0002-9939(97)03725-8
Received by editor(s): April 12, 1995
Received by editor(s) in revised form: December 1, 1995
Additional Notes: The author’s research was supported in part by an Alfred P. Sloan Foundation Doctoral Dissertation Fellowship and by NSF Grant DMS-9100148
Communicated by: Ken Goodearl
Article copyright: © Copyright 1997 American Mathematical Society