Congruence relations and direct decompositions of ordered sets. (English) Zbl 0645.06003

Kolibiar, M.

Acta Sci. Math. 51, No. 1-2, 129-135 (1987).

In the present note a notion of congruence relation is studied in the class of ordered sets which allows the same characterization of direct decompositions of directed ordered sets as in the case of algebras whenever the number of the decomposition factors is finite or the ordered set satisfies a chain condition. Moreover, it is shown that the congruence relations form a distributive lattice. Also some results on subdirect decompositions are given.

Reviewer: P.Vincke

MSC:

06A06

Partial orders, general

Keywords:

congruence relation; direct decompositions of directed ordered sets; chain condition; distributive lattice; subdirect decompositions