Ternary Semigroups and Ternary Algebras

Antoni Chronowski ()
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Antoni Chronowski: Pedagogical University

Chapter Chapter 28 in Functional Equations in Mathematical Analysis, 2011, pp 371-416 from Springer

Abstract: 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.

Keywords: Ternary semigroups of mappings; Ternary linear algebras (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-1-4614-0055-4_28

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DOI: 10.1007/978-1-4614-0055-4_28

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