Quadratic forms, division algebras and inseparable multiquadratic extensions. (Formes quadratiques, algèbres à division et extensions multiquadratiques inséparables.)
Quadratic Forms Under Algebraic Extensions.
Quantum-classical interactions and galois type extensions
An algebraic model for the relation between a certain classical particle system and the quantum environment is proposed. The quantum environment is described by the category of possible quantum states. The initial particle system is represented by an associative algebra in the category of states. The key new observation is that particle interactions with the quantum environment can be described in terms of Hopf-Galois theory. This opens up a possibility to use quantum groups in our model of particle...
Quartic exercises.
Quaternion Extensions of Order 16
2000 Mathematics Subject Classification: 12F12We describe several types of Galois extensions having as Galois group the quaternion group Q16 of order 16.This work is partially supported by project of Shumen University.
Quaternion extensions with restricted ramification
In any normal number field having Q₈, the quaternion group of order 8, as Galois group over the rationals, at least two finite primes must ramify. The classical example by Dedekind of such a field is extraordinary in that it is totally real and only the primes 2 and 3 are ramified. In this note we describe in detail all Q₈-fields over the rationals where only two (finite) primes are ramified. We also show that, for any integer n>3 and any prime , there exist unique real and complex normal number...
Quelques propriétés d’approximation reliées à la cohomologie galoisienne d’un groupe algébrique fini
On étudie différentes propriétés d’approximation pour des espaces homogènes (à stabilisateur fini) de sur un corps de nombres. On discute également du lien avec le problème de Galois inverse et on établit une formule pour le groupe de Brauer non ramifié de .