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Completion of a half linearly cyclically ordered group

Štefan Černák (2002)

Discussiones Mathematicae - General Algebra and Applications

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.

Construction of p o -groups with quasi-divisors theory

Jiří Močkoř (2000)

Czechoslovak Mathematical Journal

A method is presented making it possible to construct p o -groups with a strong theory of quasi-divisors of finite character and with some prescribed properties as subgroups of restricted Hahn groups H ( Δ , ) , where Δ are finitely atomic root systems. Some examples of these constructions are presented.

Convergence l -groups with zero radical

Ján Jakubík (1997)

Mathematica Bohemica

In this paper we investigate abelian convergence -groups with zero radical such that each bounded sequence has a convergent subsequence.

Convergence with a regulator in directed groups

Štefan Černák (2004)

Discussiones Mathematicae - General Algebra and Applications

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.

Convex lines in median groups

Milan Kolibiar (1992)

Archivum Mathematicum

There is proved that a convex maximal line in a median group G , containing 0, is a direct factor of G .

Convexities of lattice ordered groups

Ján Jakubík (1996)

Mathematica Bohemica

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 d -groups.

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