Ternary Menger hyperalgebras: some algebraic properties
DOI:
https://doi.org/10.31489/2026m2/102-118Keywords:
Menger algebras, Menger hyperalgebras, ternary Menger algebras, ternary Menger hyperalgebras, semigroups, semihypergroups, ternary semigroups, ternary semihypergroups, diagonal ternary semihypergroupsAbstract
In this article, we first establish an algebraic hyperstructure called a ternary Menger hyperalgebra of rank n, where n is a natural number. The algebraic hyperstructure can be regarded as a novel generalization of ternary semihypergroups. In particular, by setting the natural number n equal to 1, the algebraic hyperstructures of ternary Menger hyperalgebras of rank 1 and ternary semihypergroups are the same. And then, we extend some fundamental results on the ternary semihypergroup theory to study on ternary Menger hyperalgebras of rank n including subhyperalgebras and homomorphisms. Moreover, we investigate some interesting algebraic connections among Menger algebras of rank n, Menger hyperalgebras of rank n, ternary Menger algebras of rank n and ternary Menger hyperalgebras of rank n. In this section, we present that the algebraic hyperstructure of ternary Menger hyperalgebras of rank n can also be considered as an extension of the concepts Menger hyperalgebras of rank n and ternary Menger algebras of rank n. Finally, we use algebraic hyperstructures of ternary Menger hyperalgebras of rank n to construct the so-called diagonal ternary semihypergroups of the ternary Menger hyperalgebras of rank n.
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