A certain property of polynomials.
A certain property of polynomials. (Short Communication).
A Characterization of One-Element p-Bases of Rings of Constants
Let K be a unique factorization domain of characteristic p > 0, and let f ∈ K[x₁,...,xₙ] be a polynomial not lying in . We prove that is the ring of constants of a K-derivation of K[x₁,...,xₙ] if and only if all the partial derivatives of f are relatively prime. The proof is based on a generalization of Freudenburg’s lemma to the case of polynomials over a unique factorization domain of arbitrary characteristic.
A duality based proof of the combinatorial nullstellensatz.
A generalization of a second irreducibility theorem of I. Schur
A generalization of a third irreducibility theorem of I. Schur
A propos de la relation galoisienne
L’existence d’un polynôme , irréductible sur un corps de caractéristique et dont trois racines vérifient la relation linéaire , ne dépend que de la paire de groupes finis où et est le fixateur d’une racine. Le cas régulier () est désormais assez bien décrit. On démontre dans ce texte que pour de nombreuses paires primitives ( sous-groupe maximal de ) et en particulier pour toutes celles de degré , la relation n’est pas réalisable.En appendice, Joseph Oesterlé démontre que cette...
A quick and dirty irreducibility test for multivariate polynomials over .
A Simple Proof Of A Generalization Of Eisenstein's Irreducibility Criterion.
Acknowledgement of priority
Addendum to the paper: "On the number of terms of a composite polynomial" (Acta Arith. 127 (2007), 157-167)
Algebraic independence of polynomials
Algèbres de Hadamard
Algorithms for function fields.
An application of Hilbert's irreducibility theorem to diophantine equations
Autour d'un théorème de Stein.
Bounds in the theory of polynomial rings over fields. A nonstandard approach.
Calculs sur les modules projectifs
Central extensions of ordered skew fields.
Characteristic of Rings. Prime Fields
The notion of the characteristic of rings and its basic properties are formalized [14], [39], [20]. Classification of prime fields in terms of isomorphisms with appropriate fields (ℚ or ℤ/p) are presented. To facilitate reasonings within the field of rational numbers, values of numerators and denominators of basic operations over rationals are computed.