On Prüfer rings

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 ...

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 )...

Prüfer codes for acyclic hypertrees

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

On the Debate Concerning Evolutionary Search Using Prüfer Numbers

*-σ-biderivations on *-rings

Bresar in 1993 proved that each biderivation on a noncommutative prime ring is a multiple of a commutatot. A result of it is a characterization of commuting additive mappings, because each commuting additive map give rise to a biderivation. Then in 1995, he investigated biderivations, generalized biderivations and sigma-biderivations on a prime ring and generalized the results of derivations fo...