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Keywords = ternary Menger algebra

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12 pages, 282 KiB  
Article
v-Regular Ternary Menger Algebras and Left Translations of Ternary Menger Algebras
by Anak Nongmanee and Sorasak Leeratanavalee
Mathematics 2021, 9(21), 2691; https://doi.org/10.3390/math9212691 - 22 Oct 2021
Cited by 8 | Viewed by 1929
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Hypergroup Theory and Algebrization of Incidence Structures)
14 pages, 292 KiB  
Article
Ternary Menger Algebras: A Generalization of Ternary Semigroups
by Anak Nongmanee and Sorasak Leeratanavalee
Mathematics 2021, 9(5), 553; https://doi.org/10.3390/math9050553 - 5 Mar 2021
Cited by 10 | Viewed by 2654
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Algebra and Number Theory)
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