G-fonctions et théorème d'irreductibilite de Hilbert
Graded transcendental extensions of graded fields.
Groupes algébriques et équations différentielles linéaires
Le corps des séries de Puiseux généralisées
Les corps différentiellement clos dénombrables
Noether's problem for some groups of order 16n
Noncyclic Division Algebras.
Normal Polynomials in Simple Extension Fields III.
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.
Numbers with order ≤ 1
O čtrnáctém Hilbertově problému
On chains of purely transcendental field extensions
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 places of algebraic function fields.
On rank of extensions of valuations
On ruled fields
Some results and problems that arise in connection with the foundations of the theory of ruled and rational field extensions are discussed.
On subfields of
On the dimension of the space of ℝ-places of certain rational function fields
We prove that for every n ∈ ℕ the space M(K(x 1, …, x n) of ℝ-places of the field K(x 1, …, x n) of rational functions of n variables with coefficients in a totally Archimedean field K has the topological covering dimension dimM(K(x 1, …, x n)) ≤ n. For n = 2 the space M(K(x 1, x 2)) has covering and integral dimensions dimM(K(x 1, x 2)) = dimℤ M(K(x 1, x 2)) = 2 and the cohomological dimension dimG M(K(x 1, x 2)) = 1 for any Abelian 2-divisible coefficient group G.
On the extension of a valuation on a field to . - II
On the nonexcellence of field extensions .