Direct product decompositions of directed groups.

*(English)*Zbl 0713.06007The 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 |

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\textit{J. Jakubík}, Czech. Math. J. 39(114), No. 4, 618--621 (1989; Zbl 0713.06007)

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##### 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 |

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