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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Darrell Haile 1; Jung-Miao Kuo 2; Jean-Pierre Tignol 3
@article{CRMATH_2009__347_15-16_849_0, author = {Darrell Haile and Jung-Miao Kuo and Jean-Pierre Tignol}, 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}, }
Darrell Haile; Jung-Miao Kuo; Jean-Pierre Tignol. 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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.06.007/
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