Let D be a division algebra of degree 3 over a field containing a primitive cube root of unity. We give two proofs of a theorem of Rost asserting that any two Kummer elements in D can be connected by a chain of length 4.
Soit D un corps gauche de degré 3 sur un corps contenant une racine cubique de l'unité. Nous donnons deux démonstrations d'un théorème de Rost établissant que deux éléments de Kummer quelconques de D peuvent être joints par une chaine de longueur 4.
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@article{CRMATH_2009__347_15-16_849_0, author = {Haile, Darrell and Kuo, Jung-Miao and Tignol, Jean-Pierre}, title = {On chains in division algebras of degree 3}, journal = {Comptes Rendus. Math\'ematique}, pages = {849--852}, publisher = {Elsevier}, volume = {347}, number = {15-16}, year = {2009}, doi = {10.1016/j.crma.2009.06.007}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.crma.2009.06.007/} }
TY - JOUR AU - Haile, Darrell AU - Kuo, Jung-Miao AU - Tignol, Jean-Pierre TI - On chains in division algebras of degree 3 JO - Comptes Rendus. Mathématique PY - 2009 SP - 849 EP - 852 VL - 347 IS - 15-16 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2009.06.007/ DO - 10.1016/j.crma.2009.06.007 LA - en ID - CRMATH_2009__347_15-16_849_0 ER -
%0 Journal Article %A Haile, Darrell %A Kuo, Jung-Miao %A Tignol, Jean-Pierre %T On chains in division algebras of degree 3 %J Comptes Rendus. Mathématique %D 2009 %P 849-852 %V 347 %N 15-16 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2009.06.007/ %R 10.1016/j.crma.2009.06.007 %G en %F CRMATH_2009__347_15-16_849_0
Haile, Darrell; Kuo, Jung-Miao; Tignol, Jean-Pierre. On chains in division algebras of degree 3. Comptes Rendus. Mathématique, Volume 347 (2009) no. 15-16, pp. 849-852. doi : 10.1016/j.crma.2009.06.007. http://www.numdam.org/articles/10.1016/j.crma.2009.06.007/
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