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

Anak Nongmanee and Sorasak Leeratanavalee
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Anak Nongmanee: Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
Sorasak Leeratanavalee: Research Group in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand

Mathematics, 2021, vol. 9, issue 21, 1-12

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.

Keywords: ternary Menger algebras; v -regular ternary Menger algebras; left translations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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