Pure Ideals on Ordered Power Ternary Semigroups on Ternary Semihypergroups Induced by Posets

This article is devoted to the investigation of some algebraic connections between algebraic structures and algebraic hyperstructures. Firstly, we introduce the concept of ordered power ternary semigroups on ternary semihypergroups induced by posets which are generalizations of power ternary semigroups on ternary semihypergroups. Then, the ideas of ideals and pure ideals in ordered power ternary semigroups on ternary semihypergroups induced by posets are introduced. We also study some algebraic properties of pure ideals and weakly pure ideals on the ordered ternary semigroups.