Abstract We consider groups of the form $${G} = {AB}$$ G = AB with two locally cyclic subgroups A and B . The structure these is determined in cases when are both periodic or one them other not. Together a previous study case where torsion-free, this gi...

In 1918 Prüfer showed a one-to-one correspondence between labeled trees on n nodes and sequences of (n 2) node labels, obtained by iteratively deleting the leaf with the smallest label in the current tree and appending the label of the adjacent node to the code. In 1953 Neville proposed two additional methods for encoding a labeled tree of order n into a sequence of (n 2) labels. Recently, yet ...

The Algebraicity Conjecture states that a simple group of finite Morley rank should be isomorphic with an algebraic group. A program initiated by Borovik aims at controlling the 2-local structure in a hypothetical minimal counterexample to the Algebraicity Conjecture. There is now a large body of work on this program. A fundamental division arises at the outset, according to the structure of a ...

In this paper we consider five possible extensions of the Prüfer domain notion to the case of commutative rings with zero divisors and relate the corresponding properties on a ring with the property of its total ring of quotients. We show that a Prüfer ring R satisfies one of the five conditions if and only if the total ring of quotients Q(R) of R satisfies that same condition. We focus in part...

This paper studies the multiplicative ideal structure of commutative rings in which every finitely generated ideal is quasi-projective. Section 2 provides some preliminaries on quasi-projective modules over commutative rings. Section 3 investigates the correlation with well-known Prüfer conditions; namely, we prove that this class of rings stands strictly between the two classes of arithmetical...

The primary purpose of this paper is give a classification scheme for the nonzero primes of a Prüfer domain based on five properties. A prime P of a Prüfer domain R could be sharp or not sharp, antesharp or not, divisorial or not, branched or unbranched, idempotent or not. Based on these five basic properties, there are six types of maximal ideals and twelve types of nonmaximal (nonzero) primes...

The recent growing of the Semantic Web requires the need to cope with highly semantic heterogeneities among available ontologies. Ontology matching techniques aim to tackle this problem by establishing correspondences between ontologies’ elements. An intricate obstacle faces the ontology matching problem is its scalability against large number and large-scale ontologies. To tackle these challen...

M∈M2 RM whenever M1 and M2 are distinct subsets of the set of maximal ideals of R. Prüfer domains satisfying the #-condition were first studied in [9] and [10]. Domains each of whose overrings satisfy the #-condition were also studied in [10] (in the Prüfer case); these domains have come to be called ##-domains. Although the papers mentioned above contain very interesting results, those results...

This chapter describes a novel ACO algorithm for the degree-constrained minimum spanning tree (d-MST) problem. Instead of constructing the d-MST directly on the construction graph, ants construct the encoded d-MST. Two well-known tree codings are used: the Prüfer code, and the more recent Blob code (Picciotto, 1999). Both of these tree codings are bijective because they represent each spanning ...