Sur les anneaux euclidiens
Survey on Locally Factorial Krull Domains
The catenary degree of Krull monoids I
Let be a Krull monoid with finite class group such that every class contains a prime divisor (for example, a ring of integers in an algebraic number field or a holomorphy ring in an algebraic function field). The catenary degree of is the smallest integer with the following property: for each and each two factorizations of , there exist factorizations of such that, for each , arises from by replacing at most atoms from by at most new atoms. Under a very mild condition...
The first term in a minimal pure injective resolution.
The GCD property and irreducible quadratic polynomials.
The generalized Kronecker function ring and the ring R(X).
The theory of quasi-divisors on cartesian products
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.
Topologies de corps A-linéaires
Transfert de Scharlau et formes quadratiques d'enlacement dans les corps de nombres
Transforms of ideals in a commutative ring.
Two new types of rings constructed from quasiprime ideals.
Über die Berechnung von Klassenzahlen und Klassengruppen algebraischer Zahlkörper.
Un anneau de Prüfer
Let be the ring of integer valued polynomials over . This ring is known to be a Prüfer domain. But it seems there does not exist an algorithm for inverting a nonzero finitely generated ideal of . In this note we show how to obtain such an algorithm by deciphering a classical abstract proof that uses localisations of at all prime ideals of . This confirms a general program of deciphering abstract classical proofs in order to obtain algorithmic proofs.
Un exemple d'anneau caténaire
Une nouvelle caractérisation des anneaux de Prufer
v-closed ideal and Prüfer rings.
Weak Uniform Distribution of un+1 =aun + b in Dedekind Domains.
When is seminormal or -closed?
Sia a un intero algebrico con il polinomio minimale . Si danno condizioni necessarie e sufficienti affinché l'anello sia seminormale o -chiuso per mezzo di . Come applicazione, in particolare, si ottiene che se , , le condizioni sono espresse mediante il discriminante de .
When the Dual of an Ideal is a Ring.