Anneaux presque intégralement clos
Anwendung von Ideal - Transformationen.
Applications polynômiales à jacobienne constante
Approximation diophantienne dans les corps de séries en plusieurs variables
Nous montrons ici un théorème d’approximation diophantienne entre le corps des séries formelles en plusieurs variables et son complété pour la topologie de Krull.
Associate forms, joins, multiplicities and an intrinsic elimination theory
Associated primes, integral closures and ideal topologies
Let ⊆ be ideals of a Noetherian ring R, and let N be a non-zero finitely generated R-module. The set Q̅*(,N) of quintasymptotic primes of with respect to N was originally introduced by McAdam. Also, it has been shown by Naghipour and Schenzel that the set of associated primes is finite. The purpose of this paper is to show that the topology on N defined by is finer than the topology defined by if and only if is disjoint from the quintasymptotic primes of with respect to N. Moreover, we show...
Asymptotic behaviour of monomial ideals on regular sequences.
Autour des idéaux premiers de Goldman d'un anneau commutatif
Autre Demonstration du theoreme Liant regularité et paltitude en caracteristique p.
Avoidance principle and intersection property for a class of rings
Let be a commutative ring with identity. If a ring is contained in an arbitrary union of rings, then is contained in one of them under various conditions. Similarly, if an arbitrary intersection of rings is contained in , then contains one of them under various conditions.
Betti numbers and the integral closure of ideals.
Bounds for the degrees in the membership test for a polynomial ideal
Bounds in the theory of polynomial rings over fields. A nonstandard approach.
C-anneaux, E-anneaux et formule de la dimension
Carrés cartésiens et anneaux de pseudo-valuation
Carrés cartésiens et couples d'anneaux ayant les mêmes idéaux premiers
Centres and Fixed-Point Rings of Artinian Rings.
Characterization of irreducible polynomials over a special principal ideal ring
A commutative ring with unity is called a special principal ideal ring (SPIR) if it is a non integral principal ideal ring containing only one nonzero prime ideal, its length is the index of nilpotency of its maximal ideal. In this paper, we show a characterization of irreducible polynomials over a SPIR of length . Then, we give a sufficient condition for a polynomial to be irreducible over a SPIR of any length .
Classes of commutative rings characterized by going-up and going-down behavior
Clôture intégrale des idéaux et équisingularité
This text has two parts. The first one is the essentially unmodified text of our 1973-74 seminar on integral dependence in complex analytic geometry at the Ecole Polytechnique with J-J. Risler’s appendix on the Łojasiewicz exponents in the real-analytic framework. The second part is a short survey of more recent results directly related to the content of the seminar.The first part begins with the definition and elementary properties of the order function associated to an ideal of a reduced analytic...