×

zbMATH — the first resource for mathematics

Direct product decompositions of directed groups. (English) Zbl 0713.06007
The study of ordered groups always involves the interplay between the group structure and the order structure. In the paper under review the author considers a partially ordered group G such that the (G,\(\leq)\) is a directed set. The system of all congruences is used to obtain interacting examples which show that there is no possibility of sharpening the notion of congruence for directed groups in order to obtain (new) “good” relations between congruences and direct product decompositions.
Reviewer: S.P.Hurd
MSC:
06F15 Ordered groups
PDF BibTeX XML Cite
Full Text: EuDML
References:
[1] L. Fuchs: Partially ordered algebraic systems. Oxford 1969. · Zbl 0137.02001
[2] J. Jakubík: Direct decompositions of partially ordered groups. (In Russian). Czech. Math. J. 10, 231-243.
[3] J. Jakubík: On direct product decompositions of directed sets. Math. Slovaca 38, 1988, 45-49. · Zbl 0667.06001
[4] M. Kolibiar: Congruence relations and direct decompositions of ordered sets. Acta Scient. Mathem. 51, 1987, 129-135. · Zbl 0645.06003
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.