Division algebras over $C_{2}$- and $C_{3}$-fields
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- by Louis H. Rowen PDF
- Proc. Amer. Math. Soc. 130 (2002), 1607-1610 Request permission
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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Additional Information
- Louis H. Rowen
- Affiliation: Department of Mathematics & Computer Science, Bar-Ilan University, Ramat-Gan 52900, Israel
- MR Author ID: 151270
- Email: rowen@macs.biu.ac.il
- 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
- © Copyright 2001 American Mathematical Society
- 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
- MathSciNet review: 1887005