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Ternary Menger Algebras: A Generalization of Ternary Semigroups

Author

Listed:
  • Anak Nongmanee

    (M.S. Program in Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand)

  • Sorasak Leeratanavalee

    (Research Center in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand)

Abstract

Let n be a fixed natural number. Menger algebras of rank n , which was introduced by Menger, K., can be regarded as the suitable generalization of arbitrary semigroups. Based on this knowledge, an interesting question arises: what a generalization of ternary semigroups is. In this article, we first introduce the notion of ternary Menger algebras of rank n , which is a canonical generalization of arbitrary ternary semigroups, and discuss their related properties. In the second part, we establish the so-called a diagonal ternary semigroup which its operation is induced by the operation on ternary Menger algebras of rank n and then investigate their interesting properties. Moreover, we introduce the concept of homomorphism and congruences on ternary Menger algebras of rank n . These lead us to study the quotient ternary Menger algebras of rank n and to investigate the homomorphism theorem for ternary Menger algebra of rank n with respect to congruences. Furthermore, the characterization of reduction of ternary Menger algebra into Menger algebra is presented.

Suggested Citation

  • Anak Nongmanee & Sorasak Leeratanavalee, 2021. "Ternary Menger Algebras: A Generalization of Ternary Semigroups," Mathematics, MDPI, vol. 9(5), pages 1-14, March.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:5:p:553-:d:511400
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    Cited by:

    1. Anak Nongmanee & Sorasak Leeratanavalee, 2021. "v -Regular Ternary Menger Algebras and Left Translations of Ternary Menger Algebras," Mathematics, MDPI, vol. 9(21), pages 1-12, October.

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