Conservation of the noetherianity by perfect transcendental field extensions.
Construction of a controller with a generalized linear immersion
Gröbner bases for modules are used to calculate a generalized linear immersion for a plant whose solutions to its regulation equations are polynomials or pseudo-polynomials. After calculating the generalized linear immersion, we build the controller which gives the robust regulation.
Constructions of finitely generated submodules of constructively noetherian modules
Correction and Complements to "On the Symmetric and Rees Algebras of an Ideal"
Correction to: Maximal orders of global dimension and Krull dimension two.
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
Efficient generation of zero dimensional ideals in polynomial rings.
Ein Beweis des Hilbertschen Basissatzes.
Eine Anwendung des Selbergschen Siebes auf algebraische Zahlkörper
Einige Probleme der Erweiterungstheorie lokaler Ringe
Elasticity of factorizations in atomic monoids and integral domains
For an atomic domain , its elasticity is defined by : for irreducible . We study the elasticity of one-dimensional noetherian domains by means of the more subtle invariants defined by : for irreducible . As a main result we characterize all orders in algebraic number fields having finite elasticity. On the way, we obtain a series of results concerning the invariants and for monoids and integral domains which are of independent interest.
Equations for the set of overrings of normal rings and related ring extensions
We establish several finiteness characterizations and equations for the cardinality and the length of the set of overrings of rings with nontrivial zero divisors and integrally closed in their total ring of fractions. Similar properties are also obtained for related extensions of commutative rings that are not necessarily integral domains. Numerical characterizations are obtained for rings with some finiteness conditions afterwards.