Open AccessDivision algebras over ๐ถโ- and ๐ถโ-fields
Author(s) -
Louis Rowen
Publication year - 2001
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/s0002-9939-01-06277-3
Subject(s) - algorithm , annotation , computer science , artificial intelligence
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 โ 1 \sqrt {-1} is cyclic. Our methods also show any division algebra of degree 8 over a C 2 C_{2} -field containing โ 1 4 \sqrt [4 ]{-1} is cyclic.