Complete permutability of partitions in a set. I
This paper deals with directly indecomposable direct factors of a directed set.
The notion of a half lc-group G is a generalization of the notion of a half linearly ordered group. A completion of G by means of Dedekind cuts in linearly ordered sets and applying Świerczkowski's representation theorem of lc-groups is constructed and studied.
A method is presented making it possible to construct -groups with a strong theory of quasi-divisors of finite character and with some prescribed properties as subgroups of restricted Hahn groups , where are finitely atomic root systems. Some examples of these constructions are presented.
In this paper we investigate abelian convergence -groups with zero radical such that each bounded sequence has a convergent subsequence.
There is defined and studied a convergence with a fixed regulator u in directed groups. A u-Cauchy completion of an integrally closed directed group is constructed.
This paper contains a result of Cantor-Bernstein type concerning archimedean lattice ordered groups.
There is proved that a convex maximal line in a median group , containing 0, is a direct factor of .
In this paper an injective mapping of the class of all infinite cardinals into the collection of all convexities of lattice ordered groups is constructed; this generalizes an earlier result on convexities of -groups.