On Prüfer rings as images of Prüfer domains

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 ...

Prüfer codes for acyclic hypertrees

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

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 ...

On the Locality of the Prüfer Code

The Prüfer code is a bijection between trees on the vertex set [n] and strings on the set [n] of length n − 2 (Prüfer strings of order n). In this paper we examine the ‘locality’ properties of the Prüfer code, i.e. the effect of changing an element of the Prüfer string on the structure of the corresponding tree. Our measure for the distance between two trees T, T ∗ is ∆(T, T ∗) = n − 1 − |E(T )...

On the Debate Concerning Evolutionary Search Using Prüfer Numbers