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Division algebras over $C_{2}$- and $C_{3}$-fields


Author: Louis H. Rowen
Journal: Proc. Amer. Math. Soc. 130 (2002), 1607-1610
MSC (1991): Primary 11R52, 12E15, 16K20, 16K50
DOI: https://doi.org/10.1090/S0002-9939-01-06277-3
Published electronically: December 27, 2001
MathSciNet review: 1887005
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Abstract: Using elementary methods we prove a theorem of Rost, Serre, and Tignol that any division algebra of degree 4 over a $C_{3}$-field containing $\sqrt {-1}$ is cyclic. Our methods also show any division algebra of degree 8 over a $C_{2}$-field containing $\sqrt[4 ]{-1}$ is cyclic.


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

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Additional Information

Louis H. Rowen
Affiliation: Department of Mathematics & Computer Science, Bar-Ilan University, Ramat-Gan 52900, Israel
Email: rowen@macs.biu.ac.il

DOI: https://doi.org/10.1090/S0002-9939-01-06277-3
Keywords: Division algebra, cyclic, $C_{n}$-field
Received by editor(s): November 16, 2000
Received by editor(s) in revised form: January 3, 2001
Published electronically: December 27, 2001
Additional Notes: The author was supported by the Israel Science Foundation, founded by the Israel Academy of Sciences and Humanities - Center of Excellence Program no. 8007/99-3
These results were discovered following conversations with David Saltman, to whom the author expresses his thanks. The author also thanks the referee for helpful comments.
Communicated by: Lance W. Small
Article copyright: © Copyright 2001 American Mathematical Society

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