Die atomare Struktur topologischer Boolescher Ringe und s-beschränkter Inhalte
Die strenge Approximationseigenschaft lokaler Ringe.
Direct Limits of Power Series Rings.
Discrete valuation domains and ranks of their maximal extension
Division dans l'anneau des séries formelles à croissance contrôlée. Applications
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 a Weierstrass-Hironaka division theorem for such subrings. Moreover, given an ideal ℐ of A and a series f in A we prove the existence in A of a unique remainder r modulo ℐ. As a consequence, we get a new proof of the noetherianity of A.
Dualità sul completamento naturale di un anello noetheriano
Dualité dans les modules topologiques.
Soit I un ensembre quelconque. Si M est un sous-module quelconque de A1 et N un sous-module de Mx, α-dual de M (Mazan 1976), le dual topologique de M, muni de la topologie faible, Ts(N), est, sous certaines conditions, isomorphe topologiquement à N/M⊥. Ce résultat peut s'étendre au cas où M et N sont deux modules quelconques en dualité. Cette note étudie aussi les topologies Tℑ de M, compatibles avec la dualité et introduit la notion de topologie uniforme.
Ein Beweis des Hilbertschen Basissatzes.
Eine Anwendung des Selbergschen Siebes auf algebraische Zahlkörper
Einige Bemerkungen zur Struktur lokaler Henselscher Ringe
Equivalent Categories of Divisible Modules.
Ergänzung und Berichtigung zu : Die Zahl der Spitzen und die Jacobi-Algebra einer isolierten Hyperflächensingularität.
Errata to the paper "Remarks of the elementary theories of formal and convergent power series" Fundamenta Mathematicae 105 (1980), pp. 229-239
Erratum : Compactifications de Bohr d'anneaux et de modules
Etale cohomology of henselian rings and cohomology of abstract Riemann surfaces of fields.
Exponential Automorphisms of Complete Local Rings.
Exposé on a conjecture of Tougeron
An algebra homomorphism of the locatized affine rings of an algebraic variety is continuous in the Krull topology of the respective local rings. It is not necessarily open or closed in the Krull topology. However, we show that the induced map on the associated analytic local rings is also open and closed in the Krull topology. To do this we prove a conjecture of Tougeron which states that if is an analytic curve on an analytic variety and is a formal power series which is convergent when restricted...
Extension d'un théorème de Pólya-Cantor à des séries rationnelles en variables non commutatives
Extension of the Two-Variable Pierce-Birkhoff conjecture to generalized polynomials
Let be a continuous, piecewise-polynomial function. The Pierce-Birkhoff conjecture (1956) is that any such is representable in the form , for some finite collection of polynomials . (A simple example is .) In 1984, L. Mahé and, independently, G. Efroymson, proved this for ; it remains open for . In this paper we prove an analogous result for “generalized polynomials” (also known as signomials), i.e., where the exponents are allowed to be arbitrary real numbers, and not just natural numbers;...
Factorisation de suites récurrentes linéaires et applications