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September 10, 2025Open Access

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

Key Points

The study introduces ordered power ternary semigroups defined through posets and their properties.
It explores the concepts of pure ideals within these algebraic structures, enhancing understanding of their interrelations.
Weakly pure ideals are examined, adding depth to the existing theories on algebraic connections.
Investigating the algebraic properties of these structures offers new insights into their classification and application.

Abstract

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.

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

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Abstract

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