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Ternary Semigroups and Ternary Algebras

In: Functional Equations in Mathematical Analysis

Author

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  • Antoni Chronowski

    (Pedagogical University)

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.

Suggested Citation

  • Antoni Chronowski, 2011. "Ternary Semigroups and Ternary Algebras," Springer Optimization and Its Applications, in: Themistocles M. Rassias & Janusz Brzdek (ed.), Functional Equations in Mathematical Analysis, chapter 0, pages 371-416, Springer.
    • Handle: RePEc:spr:spochp:978-1-4614-0055-4_28
    DOI: 10.1007/978-1-4614-0055-4_28
    as

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