Décompositions primaires dans les catégories de Grothendieck commutatives. II.
Décompositions primaires dans les catégories de Grothendieck commutatives. I.
Derivations and Deformations of Artinian Algebras
Des anneaux aux conditions des chaines ascendantes sur les idéaux de type n.
Differential rings in which any ideal is differential
Dimension and attached primes of an Artinian module
Direct Limits of Power Series Rings.
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