n-Prüfer domains

. A C ] 2 1 N ov 2 00 6 FACTORING IDEALS IN PRÜFER DOMAINS

We show that in certain Prüfer domains, each nonzero ideal I can be factored as I = I v Π, where I v is the divisorial closure of I and Π is a product of maximal ideals. This is always possible when the Prüfer domain is h-local, and in this case such factorizations have certain uniqueness properties. This leads to new characterizations of the h-local property in Prüfer domains. We also explore ...

A "υ-Operation Free" Approach to Prüfer υ-Multiplication Domains

The so-called Prüfer υ-multiplication domains PυMDs are usually defined as domains whose finitely generated nonzero ideals are t-invertible. These domains generalize Prüfer domains and Krull domains. The PυMDs are relatively obscure compared to their verywell-known special cases. One of the reasons could be that the study of PυMDs uses the jargon of star operations, such as the υ-operation and ...

Prüfer codes for acyclic hypertrees

We describe a new Prüfer code based on star-reductions which works for infinite acyclic hypertrees.

Curves and coherent Prüfer rings

Usual definitions of Dedekind domain are not well suited for an algorithmic treatment. Indeed, the notion of Noetherian rings is subtle from a constructive point of view, and to be able to get prime ideals involve strong hypotheses. For instance, if k is a field, even given explicitely, there is in general no method to factorize polynomials in k[X]. The work [2] analyses the notion of Dedekind ...

ar X iv : m at h / 06 06 67 1 v 1 [ m at h . A C ] 2 7 Ju n 20 06 PRÜFER ⋆ – MULTIPLICATION DOMAINS AND ⋆ – COHERENCE