Regularity in Ternary Semihypergroups Induced by Subsets of Ternary Semigroups

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.