Division algebras over πΆβ- and πΆβ-fields
Louis Halle Rowen Β· Proceedings of the American Mathematical Society Β· 2001
Using elementary methods we prove a theorem of Rost, Serre, and Tignol that any division algebra of degree 4 over a C 3 C_{3} -field containing β 1 \sqrt {-1} is cyclic. Our methods also show any division algebra of degree 8 over a C 2 C_{2} -field containing β 1 4 \sqrt [4 ]{-1} is cyclic.