Algèbres de Hadamard
Composite rational functions expressible with few terms
We consider a rational function which is ‘lacunary’ in the sense that it can be expressed as the ratio of two polynomials (not necessarily coprime) having each at most a given number of terms. Then we look at the possible decompositions , where are rational functions of degree larger than 1. We prove that, apart from certain exceptional cases which we completely describe, the degree of is bounded only in terms of (and we provide explicit bounds). This supports and quantifies the intuitive...
Erratum. Quelques remarques sur le -invariant
Factorisation de Ritt pour les polynômes exponentiels formels
Fields of characteristic 2 with prescribed u-invariants.
Functions without residue and a bilinear differential equation
Lagrange Resolvents.
Medial subcartesian products of fields
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 un article de Sharif et Woodcock
H. Sharif et C. Woodcock donnent dans [26] une caractérisation des séries formelles à coefficients dans un corps de caractéristique non nulle et algébriques sur ; ils en déduisent simplement l’algébricité du produit de Hadamard ou des diagonales de séries algébriques. (Ces résultats ont aussi été obtenus par T. Harase [14]). Nous donnons ici une démonstration légèrement différente de leur théorème et montrons comment on peut en déduire une généralisation intéressante de la notion de -substitution...
On mulitplication and factorization of polynomials, II. Irreducibility discussion.
On multiplication and factorization of polynomials, I. Lexicographic orderings and extreme aggregates of terms.
On polynomial transformations in several variables
Periodic points, multiplicities, and dynamical units.
Pfister's Dimension and the Level of Fields.
Poznámka o jednej vlastnosti dvojprvkového telesa
Principal ideal theorems for holomorphy rings in fields.
Quadratische Räume unendlicher Dimension und partielle Isomorphismen.
Quelques remarques sur le -invariant
Rational Puiseux expansions