The solution of the A T-system for arbitrary boundary.
The Strong Anick Conjecture is true
Recently Umirbaev has proved the long-standing Anick conjecture, that is, there exist wild automorphisms of the free associative algebra over a field of characteristic 0. In particular, the well-known Anick automorphism is wild. In this article we obtain a stronger result (the Strong Anick Conjecture that implies the Anick Conjecture). Namely, we prove that there exist wild coordinates of . In particular, the two nontrivial coordinates in the Anick automorphism are both wild. We establish a...
The Structure of Certain Ideal Transforms.
The theory of quasi-divisors on cartesian products
The valuated ring of the arithmetical functions as a power series ring
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.
The Waring loci of ternary quartics.
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...
Thom-Boardman singularities and monoidal transforms
Tight closure of parameter ideals.
Topological characterizations of ordered groups with quasi-divisor theory
For an order embedding of a partly ordered group into an -group a topology is introduced on which is defined by a family of valuations on . Some density properties of sets , and ( being -ideals in ) in the topological space are then investigated, each of them being equivalent to the statement that is a strong theory of quasi-divisors.
Topological computation of local cohomology multiplicities.
We express the Lyubeznik numbers of the local ring of a complex isolated singularity in terms of Betti numbers of the associated real link.
Topologies de corps A-linéaires
Totally indefinite Euclidean quaternion fields
We study the Euclidean property for totally indefinite quaternion fields. In particular, we establish a complete list of norm-Euclidean such fields over imaginary quadratic number fields. This enables us to exhibit an example which gives a negative answer to a question asked by Eichler. The proofs are both theoretical and algorithmic.
Toward an arithmetic of polynomials.
Transfer of the notion of -rings to fibre products. (Transfert de la notion de -anneaux aux produits fibres.)
Transfert de Scharlau et formes quadratiques d'enlacement dans les corps de nombres
Transforms of ideals in a commutative ring.
Treillis d'idéaux et structure d'anneaux
Trivial formal fibres and formal Laurent series