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On direct and subdirect product decompositions of partially ordered sets. (English) Zbl 1016.06002
The paper deals with possibilities of direct and subdirect product decompositions of some types of partially ordered sets. The author characterizes lattices which are internal direct products of their convex sublattices with given central elements. Further, he proves that directed sets of finite length satisfy the strong cancellation rule. The notion of a regular subdirect decomposition of a semilattice is introduced and a cancellation rule for some kind of such decompositions of semilattices is proved.

##### MSC:
 06A06 Partial orders, general 06A12 Semilattices 06B05 Structure theory of lattices
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##### References:
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