An Innovative Technique for Various Types of Tri Ideals in b-Semirings

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DOI: https://doi.org/10.28924/2291-8639-23-2025-115
Published: May 16, 2025
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Salahuddin, M. Suguna, K. Saranya, An Innovative Technique for Various Types of Tri Ideals in b-Semirings, Int. J. Anal. Appl., 23 (2025), 115.

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Salahuddin, M. Suguna, K. Saranya

Abstract

This paper explores the structural complexities of tri-ideals and quasi-ideals within b-semirings. We provide characterizations of tri-ideals in b-semirings and define their significant algebraic properties. We investigate the properties of S tri-ideals and their implications in algebra. By emphasizing the algebraic coherence of these structures, we demonstrate how the intersection of 1-left tri-ideals and right ideals can be used to generate a 1-left tri-ideal. We also provide relevant examples for better understanding. Additionally, we rigorously establish key theorems for various scenarios involving tri-ideal, highlighting their theoretical foundations. The main motivation for this study is to emphasize the growing importance of tri-ideal categories over b-semirings in the real algebraic structures.

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