Regularity in Ternary Semihypergroups Induced by Subsets of Ternary Semigroups: Annual Meeting in Mathematics 2023 - Nongmanee, Anak; Leeratanavalee, Sorasak (Thai Journal of Mathematics, 2024)
Ternary semihypergroups, which can be considered as a generalization of arbitrary ternary semigroups, are algebraic hyperstructures together with one ternary associative hyperoperation. In this article, we construct a new algebraic hyperstructure which can be formed as a ternary semihypergroup. In particularly, such a ternary semihypergroup is induced by a nonempty subset of the base set of the ternary semigroup. We investigate the regularity of the ternary semihypergroups. Furthermore, we present some of its characterizations via significant conditions.