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ISSN 1088-6826(e) ISSN 0002-9939(p)

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

Author(s): Louis H. Rowen
Journal: Proc. Amer. Math. Soc. 130 (2002), 1607-1610.
MSC (1991): Primary 11R52, 12E15, 16K20, 16K50
Posted: 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:

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4.: Artin M., Brauer-Severi varieties, Brauer Groups in Ring Theory and Algebraic Geometry, Springer Lecture Notes in Math., vol. 917, Springer, Berlin, New York, 1982, pp. 194-210. MR 83j:14015
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7.: Rost M., Serre J.P., and Tignol J.P., The trace form of a central simple algebra of degree four, paper in preparation.
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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: 10.1090/S0002-9939-01-06277-3
PII: S 0002-9939(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
Posted: 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
Copyright of article: Copyright 2001, American Mathematical Society

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