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v -Regular Ternary Menger Algebras and Left Translations of Ternary Menger Algebras

Author

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  • Anak Nongmanee

    (Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
    These authors contributed equally to this work.)

  • Sorasak Leeratanavalee

    (Research Group in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
    These authors contributed equally to this work.)

Abstract

Let n be a fixed natural number. Ternary Menger algebras of rank n , which was established by the authors, can be regarded as a suitable generalization of ternary semigroups. In this article, we introduce the notion of v -regular ternary Menger algebras of rank n , which can be considered as a generalization of regular ternary semigroups. Moreover, we investigate some of its interesting properties. Based on the concept of n -place functions ( n -ary operations), these lead us to construct ternary Menger algebras of rank n of all full n -place functions. Finally, we study a special class of full n -place functions, the so-called left translations. In particular, we investigate a relationship between the concept of full n -place functions and left translations.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:21:p:2691-:d:662947
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    References listed on IDEAS

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    1. Anak Nongmanee & Sorasak Leeratanavalee, 2021. "Ternary Menger Algebras: A Generalization of Ternary Semigroups," Mathematics, MDPI, vol. 9(5), pages 1-14, March.
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