Eine Anwendung des Selbergschen Siebes auf algebraische Zahlkörper
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
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
Factorisation de suites récurrentes linéaires et applications
Fields: Algebraically closed and others.
Fonctions analytiques dans le complémentaire d'une famille de disques
Formal power series rings over a -domain
Formal relations between quasianalytic functions of some fixed class
In [Ga] Gabrielov has given conditions under which the completion of the kernel of a morphism φ: A → B between analytic rings coincides with the kernel of the induced morphism φ̂: Â → B̂ between the completions. If B is a domain, a sufficient condition is that rk φ = dim(Â/ker φ̂), where rk φ is the rank of the jacobian matrix of φ considered as a matrix over the quotient field of B. We prove that the above property holds in a fixed quasianalytic Denjoy-Carleman class if and only if the class coincides...
Fréchet algebras of power series
We consider Fréchet algebras which are subalgebras of the algebra 𝔉 = ℂ [[X]] of formal power series in one variable and of 𝔉ₙ = ℂ [[X₁,..., Xₙ]] of formal power series in n variables, where n ∈ ℕ. In each case, these algebras are taken with the topology of coordinatewise convergence. We begin with some basic definitions about Fréchet algebras, (F)-algebras, and other topological algebras, and recall some of their properties; we discuss Michael's problem from 1952 on the continuity of characters...
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.
Gabrielov's Rank Condition is Equivalent to an Inequality of Reduced Orders.
Géométrie analytique rigide d'après Tate, Kiehl...
Groupes de Picard et séries formelles
Hadamard operations on rational functions
Höhere Derivationen und Regularität.
Intégration sur un cycle évanescent.
Iterations and logarithms of formal automorphisms. (Short Communication).
Japanische und ausgezeichnete lokale Ringe.