Normalbasis bei Körpern ohne höhere Verzweigung.
Norms in Quadratic Fields and Their Relations to Non Commuting 2x2 Matrices I.
Note on a variation of the Schröder-Bernstein problem for fields
In this note we study fields with the property that the simple transcendental extension of is isomorphic to some subfield of but not isomorphic to . Such a field provides one type of solution of the Schröder-Bernstein problem for fields.
Note sur les relations entre les racines d’un polynôme réductible
Dans cet article, nous exploitons la réductibilité d’un polynôme d’une variable pour calculer efficacement l’idéal des relations algébriques entre ses racines.
Note sur les relations entre les racines d'un polynôme réductible
Dans cet article, nous exploitons la réductibilité d'un polynôme d'une variable pour calculer efficacement l'idéal des relations algébriques entre ses racines.
Numbers with order ≤ 1
O čtrnáctém Hilbertově problému
Odd parts of tame kernels of dihedral extensions
On a theorem of Ritt and related Diophantine problems.
On algebraic closures.
This is a description of some different approaches which have been taken to the problem of generalizing the algebraic closure of a field. Work surveyed is by Enoch and Hochster (commutative algebra), Raphael (categories and rings of quotients), Borho (the polynomial approach), and Carson (logic).Later work and applications are given.
On certain algebraic curves related to polynomial maps
On chains of purely transcendental field extensions
On degrees of three algebraic numbers with zero sum or unit product
Let α, β and γ be algebraic numbers of respective degrees a, b and c over ℚ such that α + β + γ = 0. We prove that there exist algebraic numbers α₁, β₁ and γ₁ of the same respective degrees a, b and c over ℚ such that α₁ β₁ γ₁ = 1. This proves a previously formulated conjecture. We also investigate the problem of describing the set of triplets (a,b,c) ∈ ℕ³ for which there exist finite field extensions K/k and L/k (of a fixed field k) of degrees a and b, respectively, such that the degree of the...
On dihedral algebraic function fields
On double covers of the generalized alternating group as Galois groups over algebraic number fields
Let mℤd ≀ mℤd ≀ mℤd ≀ m
On elementary equivalence, isomorphism and isogeny
Motivated by recent work of Florian Pop, we study the connections between three notions of equivalence of function fields: isomorphism, elementary equivalence, and the condition that each of a pair of fields can be embedded in the other, which we call isogeny. Some of our results are purely geometric: we give an isogeny classification of Severi-Brauer varieties and quadric surfaces. These results are applied to deduce new instances of “elementary equivalence implies isomorphism”: for all genus zero...
On extensions of the maximal cyclotomic field having a given classical Galois group.
On finite linear groups stable under Galois operation.
On Galois cohomology and realizability of 2-groups as Galois groups II
In [Michailov I.M., On Galois cohomology and realizability of 2-groups as Galois groups, Cent. Eur. J. Math., 2011, 9(2), 403–419] we calculated the obstructions to the realizability as Galois groups of 14 non-abelian groups of order 2n, n ≥ 4, having a cyclic subgroup of order 2n−2, over fields containing a primitive 2n−3th root of unity. In the present paper we obtain necessary and sufficient conditions for the realizability of the remaining 8 groups that are not direct products of smaller groups....
On Galois cohomology and realizability of 2-groups as Galois groups
In this paper we develop some new theoretical criteria for the realizability of p-groups as Galois groups over arbitrary fields. We provide necessary and sufficient conditions for the realizability of 14 of the 22 non-abelian 2-groups having a cyclic subgroup of index 4 that are not direct products of groups.