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Convex isomorphisms of directed multilattices. (English) Zbl 0802.06008
To each direct product decomposition of a partially ordered set $$L$$ and each element $$s^ 0\in L$$ there corresponds an internal direct product decomposition of $$L$$ with the central element $$s^ 0$$. By applying the notion of an internal direct product decomposition, the authors investigate the relations between convex isomorphisms and direct product decompositions of directed multilattices. In this paper, they generalize the main result from M. Kolibiar and J. Lihová [Math. Slovaca 43, No. 4, 417-425 (1993; Zbl 0797.06004), Theorem 10] in two directions. It is proved that this result is true in the case when $$L$$ is a direct product of directly indecomposable lattices; the number of these lattices may be arbitrary. Next, it is shown that the result remains valid for the case of directed multilattices.

##### MSC:
 06B99 Lattices 06A99 Ordered sets