Parallélogrammes galoisiens infinis
Plongeants d'extensions galoisiennes
Polynomial Imaginary Decompositions for Finite Separable Extensions
Let K be a field and let L = K[ξ] be a finite field extension of K of degree m > 1. If f ∈ L[Z] is a polynomial, then there exist unique polynomials such that . A. Nowicki and S. Spodzieja proved that, if K is a field of characteristic zero and f ≠ 0, then have no common divisor in of positive degree. We extend this result to the case when L is a separable extension of a field K of arbitrary characteristic. We also show that the same is true for a formal power series in several variables....
Polynomial subfields of k (x).
Polynomials over solving an embedding problem
The fields defined by the polynomials constructed in E. Nart and the author in J. Number Theory 16, (1983), 6–13, Th. 2.1, with absolute Galois group the alternating group , can be embedded in any central extension of if and only if , or and is a sum of two squares. Consequently, for theses values of , every central extension of occurs as a Galois group over .
Polynomials whose Galois groups are Frobenius groups with prime order complement
We give an effective characterization theorem for integral monic irreducible polynomials of degree whose Galois groups over are Frobenius groups with kernel of order and complement of prime order.
Precise study of some number fields and Galois actions occurring in conformal field theory
Prehomogeneous vector spaces and field extensions.
Primitive elements in rings of holomorphic functions.
Pro-2-Demuskin groups of rank ...0 as Galois groups of maximal 2-extensions of fields.
Problème de plongement et contraintes galoisiennes sur le groupe des classes
Pro-p Galois groups of rank ... 4.
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.
Random Galois extensions of Hilbertian fields
Let be a Galois extension of a countable Hilbertian field . Although need not be Hilbertian, we prove that an abundance of large Galois subextensions of are.
Realisierung endlicher Gruppen als Galoisgruppen.
Realizing dyadic factors of elementary type Witt rings and pro-2 Galois groups.
Relative Spectral Norm on Algebraic Numbers
Remarques sur la structure galoisienne des unités des corps de nombres
Roots of Unity over Large Algebraic Fields.