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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Wang counterexamples lead to noncrossed products
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by Eric S. Brussel PDF
Proc. Amer. Math. Soc. 125 (1997), 2199-2206 Request permission

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
  • 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
  • © Copyright 1997 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 125 (1997), 2199-2206
  • MSC (1991): Primary 16S35; Secondary 11R37
  • DOI: https://doi.org/10.1090/S0002-9939-97-03725-8
  • MathSciNet review: 1371116