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On ternary semigroups of homomorphisms of ordered sets. (English) Zbl 0812.08006

In many areas of mathematics the mutual connections between algebraic, ordered, topological structures and semigroups (groups) of some mappings of these structures are studied. In the present paper we introduce the notion of a ternary semigroup of homomorphisms of ordered sets which is the counterpart of a semigroup of endomorphisms of an ordered set. In the main theorem we give necessary and sufficient conditions for a certain characterization of ordered sets by means of ternary semigroups of homomorphisms of these sets.

MSC:

08A62 Finitary algebras
20N15 \(n\)-ary systems \((n\ge 3)\)
06A06 Partial orders, general
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