Given an algebraically closed field K of characteristic zero, we prove the Abhyankar-Jung theorem for any excellent henselian ring whose completion is a formal power series ring K[[z]]. In particular, examples include the local rings which form a Weierstrass system over the field K.
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...
The paper examines the ring of arithmetical functions, identifying it to the domain of formal power series over in a countable set of indeterminates. It is proven that is a complete ultrametric space and all its continuous endomorphisms are described. It is also proven that is a quasi-noetherian ring.
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.
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...
We express the Lyubeznik numbers of the local ring of a complex isolated singularity in terms of Betti numbers of the associated real link.