Displaying similar documents to “The non-archimedean Corona problem”

One-fibered ideals in 2-dimensional rational singularities that can be desingularized by blowing up the unique maximal ideal

Veronique Lierde (2011)

Open Mathematics

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Let (R;m) be a 2-dimensional rational singularity with algebraically closed residue field and whose associated graded ring is an integrally closed domain. Göhner has shown that for every prime divisor v of R, there exists a unique one-fibered complete m-primary ideal A v in R with unique Rees valuation v and such that any complete m-primary ideal with unique Rees valuation v, is a power of A v. We show that for v ≠ ordR, A v is the inverse transform of a simple complete ideal in an immediate...

When is Z α seminormal or t -closed?

Martine Picavet-L'Hermitte (1999)

Bollettino dell'Unione Matematica Italiana

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Sia a un intero algebrico con il polinomio minimale f X . Si danno condizioni necessarie e sufficienti affinché l'anello Z α sia seminormale o t -chiuso per mezzo di f X . Come applicazione, in particolare, si ottiene che se f X = X 3 + a X + b , a , b Z le condizioni sono espresse mediante il discriminante de f X .

Separating ideals in dimension 2.

James J. Madden, Niels Schwartz (1997)

Revista Matemática de la Universidad Complutense de Madrid

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Experience shows that in geometric situations the separating ideal associated with two orderings of a ring measures the degree of tangency of the corresponding ultrafilters of semialgebraic sets. A related notion of separating ideals is introduced for pairs of valuations of a ring. The comparison of both types of separating ideals helps to understand how a point on a surface is approached by different half-branches of curves.