Division algebras over 𝐶₂- and 𝐶₃-fields

Rowen, Louis

doi:10.1090/S0002-9939-01-06277-3

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

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