Finiteness theorems for factorizations.
Fonctions à valeurs entières et module de Carlitz
Soient le module de Carlitz, un polynôme de et l’ensemble . Nous montrons qu’une fonction entière de type quadratique qui prend des valeurs entières sur , est polynomiale. De plus, la borne est optimale. Ceci est un analogue en caractéristique finie du théorème de Gel’fond-Pólya.
Fonctions arithmétiques [Book]
Fonctions pseudo-concaves et anneaux henséliens
Formal prime ideals of infinite value and their algebraic resolution
Suppose that is a local domain essentially of finite type over a field of characteristic , and a valuation of the quotient field of which dominates . The rank of such a valuation often increases upon extending the valuation to a valuation dominating , the completion of . When the rank of is , Cutkosky and Ghezzi handle this phenomenon by resolving the prime ideal of infinite value, but give an example showing that when the rank is greater than , there is no natural ideal in that...
Formes d'inertie et complexe de Koszul associés à des polynômes plurihomogènes.
The existence of common zero of a family of polynomials has led to the study of inertial forms, whose homogeneous part of degree 0 constitutes the ideal resultant. The Kozsul and Cech cohomologies groups play a fundamental role in this study. An analogueous of Hurwitz theorem is given, and also, one finds a N. H. McCoy theorem in a particular case of this study.
Fractions rationnelles à valeurs entières
Fragmented integral domains
Fréchet algebras, formal power series, and automatic continuity
We describe all those commutative Fréchet algebras which may be continuously embedded in the algebra ℂ[[X]] in such a way that they contain the polynomials. It is shown that these algebras (except ℂ[[X]] itself) always satisfy a certain equicontinuity condition due to Loy. Using this result, some applications to the theory of automatic continuity are given; in particular, the uniqueness of the Fréchet algebra topology for such algebras is established.
Free minimal resolutions and the Betti numbers of the suspension of an -gon.
Full Ideals of Polynomial Rings.
Functions without residue and a bilinear differential equation
Functorial Subgroups Commuting with Inverse Limits.
Further remarks on formal power series
In this paper, we present a considerable simplification of the proof of a theorem by Gan and Knox, stating a sufficient and necessary condition for existence of a composition of two formal power series. Then, we consider the behavior of such series and their (formal) derivatives at the boundary of the convergence circle, obtaining in particular a theorem of Bugajewski and Gan concerning the structure of the set of points where a formal power series is convergent with all its derivatives.
Gabriel dimension of graded rings
Galois modules and embedding problems.
Ganzalgebraische Punkte und der Hilbertsche Irreduzibilitätssatz.
Gaussian and Prüfer conditions in bi-amalgamated algebras
Let and be two ring homomorphisms and let and be ideals of and , respectively, such that . In this paper, we investigate the transfer of the notions of Gaussian and Prüfer rings to the bi-amalgamation of with along with respect to (denoted by introduced and studied by S. Kabbaj, K. Louartiti and M. Tamekkante in 2013. Our results recover well known results on amalgamations in C. A. Finocchiaro (2014) and generate new original examples of rings possessing these properties.
Generalized equivalence of matrices over Prüfer domains.
Generalized GCD rings.