Abstract
The ternary algebraic, topological, ordered structures are used in the modern theoretical and mathematical physics and in the theory of functional equations. The subject-matter of this paper focuses on ternary semigroups of mappings and ternary algebras of mappings. The main theorem states that every n-ary (ternary) semigroup is embeddable into an n-ary (ternary) semigroup of mappings. The analysis of the structure of ternary semigroups of mappings by means of the Green’s relations shows that these algebraic structures are a natural generalization of (binary) semigroups of mappings. The ternary semigroups of mappings are used for constructing the natural examples of ternary algebras, which are the counterparts of binary algebras.
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