EuDML | Browse

Page 1

Displaying 1 – 5 of 5

Plongement d'une extension diédrale dans une extension diédrale ou quaternionienne

Bernadette Perrin-Riou (1980)

Annales de l'institut Fourier

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.

Polynomials and degrees of maps in real normed algebras

Takis Sakkalis (2020)

Communications in Mathematics

Let $𝒜$ be the algebra of quaternions $ℍ$ or octonions $𝕆$ . In this manuscript an elementary proof is given, based on ideas of Cauchy and D’Alembert, of the fact that an ordinary polynomial $f (t) \in 𝒜 [t]$ has a root in $𝒜$ . As a consequence, the Jacobian determinant $| J (f) |$ is always non-negative in $𝒜$ . Moreover, using the idea of the topological degree we show that a regular polynomial $g (t)$ over $𝒜$ has also a root in $𝒜$ . Finally, utilizing multiplication ( $*$ ) in $𝒜$ , we prove various results on the topological degree of products...

Displaying 1 – 5 of 5

Plongement d'une extension diédrale dans une extension diédrale ou quaternionienne

Polynomials and degrees of maps in real normed algebras

Polynomials and Vandermonde matrices over the field of quaternions.

Potenzen von Galoisfeldern.

Prime factorization of integral Cayley octaves

Currently displaying 1 – 5 of 5