On utilise les méthodes de Neukirch et Poitou pour écrire les conditions locales et globales des problèmes de plongement. Le cas étudié ici est celui du plongement d’une extension diédrale dans une extension diédrale ou quaternionienne, le corps de base étant un corps de nombres.
Let be the algebra of quaternions or octonions . In this manuscript an elementary proof is given, based on ideas of Cauchy and D’Alembert, of the fact that an ordinary polynomial has a root in . As a consequence, the Jacobian determinant is always non-negative in . Moreover, using the idea of the topological degree we show that a regular polynomial over has also a root in . Finally, utilizing multiplication () in , we prove various results on the topological degree of products...