The distributivity property of finite intersections of valuation rings
The distributivity property of valuation rings
The hierarchy of uniserial modules over a valuation domain.
The Krull-Schmidt theorem for categories of finitely generated modules over valuation domains.
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.
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.
Topologies de corps A-linéaires
Treillis d'idéaux et structure d'anneaux