Ordered Pseudo-Ideals of An Ordered Ternary Semigroup

Objectives: This research explores the concept of ordered pseudo-ideals in an ordered ternary semigroup 𝐺, which builds on the existing idea of pseudoideals in a semigroup. Methods: The investigation delves into some unique properties of ordered pseudo-ideals in an ordered ternary semigroup 𝐺. Findings: This study has established many sufficient conditions for (𝐿𝑀𝑁] to be an ordered pseudo-ideal of 𝐺 where 𝐿, 𝑀 and 𝑁 are non-empty subsets of 𝐺. Additionally, the study provides conditions for subsets (𝐿𝐵𝐵] and (𝐵𝐵𝐿] to be recognized as ordered left and right pseudo-ideals, respectively, as well as ordered bi-ideals within 𝐺. Novelty: This contributes to a deeper understanding of ideal theory in structured algebraic systems and offers insights that could be beneficial to abstract algebra and theoretical computer science. This advancement in understanding how algebraic structures can be ordered and organized opens up new possibilities for applying these concepts in various mathematical and computational theories. Keywords: Ordered Ternary Semigroup; Commutative Ordered Ternary Semigroup; Ordered Ideal; Ordered Pseudo-ideal; Ordered Bi-ideal