Year: 2025
Type: article
Abstract: Objectives: This research explores the concept of ordered pseudo-ideals in an ordered ternary semigroup πΊ, 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 πΊ. Findings: This study has established many sufficient conditions for (πΏππ] to be an ordered pseudo-ideal of πΊ where πΏ, π and π are non-empty subsets of πΊ. Additionally, the study provides conditions for subsets (πΏπ΅π΅] and (π΅π΅πΏ] to be recognized as ordered left and right pseudo-ideals, respectively, as well as ordered bi-ideals within πΊ. 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
Authors: Dattatray N Shinde, Machchhindra T Gophane, Manish C Agalave
Institutions: Shivaji University, Fergusson College
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4407611264