The Global Homological Dimension of Some Algebras of Differential Operators.
The ring of arithmetical functions with unitary convolution: Divisorial and topological properties
We study , the ring of arithmetical functions with unitary convolution, giving an isomorphism between and a generalized power series ring on infinitely many variables, similar to the isomorphism of Cashwell-Everett [NumThe] between the ring of arithmetical functions with Dirichlet convolution and the power series ring on countably many variables. We topologize it with respect to a natural norm, and show that all ideals are quasi-finite. Some elementary results on factorization into atoms...
Théorème de Kaplansky effectif pour des valuations de rang 1 centrées sur des anneaux locaux réguliers et complets
On montre que tout anneau local régulier complet muni d’une valuation de rang peut être plongé, en tant qu’anneau valué, dans un anneau de séries de Puiseux généralisées.
Théorèmes de préparation Gevrey et étude de certaines applications formelles
We consider subrings A of the ring of formal power series. They are defined by growth conditions on coefficients such as, for instance, Gevrey conditions. We prove preparation theorems of Malgrange type in these rings. As a consequence we study maps F from to without constant term such that the rank of the Jacobian matrix of F is equal to 1. Let be a formal power series. If F is a holomorphic map, the following result is well known: ∘ F is analytic implies there exists a convergent power series...
Théorie des modèles pour des anneaux de fonctions entières et des corps de fonctions méromorphes
Topological -adic vector spaces and index theory
Two iterative functional equations for power series.
Two iterative functional equations for power series. (Short Communication).