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

Salahuddin, Salahuddin; Suguna, M.; Saranya, K.

doi:10.28924/2291-8639-23-2025-115

Research Article

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

Salahuddin Salahuddin*
M. Suguna
K. Saranya

* Corresponding author

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.

How to Cite

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

BibTeX

@article{Salahuddin2025,
  author  = {Salahuddin, Salahuddin and Suguna, M. and Saranya, K.},
  title   = {An Innovative Technique for Various Types of Tri Ideals in b-Semirings},
  journal = {Int. J. Anal. Appl.},
  volume  = {23},
  year    = {2025},
  pages   = {115},
  doi     = {10.28924/2291-8639-23-2025-115}
}

References

[1] K. Arulmozhi, The Algebraic Theory of Semigroups and Semirings, LAP Lambert Academic Publishing, 2019.
[2] K. Arulmozhi, New Approach of Various Ideals in Ternary Semirings, J. Xidian Univ. 14 (2020), 22–29.
[3] V.R. Daddi, Y.S. Pawar, On Completely Regular Ternary Semiring, Novi Sad J. Math. 42 (2012), 1–7.
[4] M.K. Dubey, Anuradha, A Note on Prime Quasi-Ideals in Ternary Semirings, Kragujevac J. Math. 37 (2013), 361–367.
[5] T.K. Dutta, S. Kar, On Regular Ternary Semirings, in: Advances in Algebra, World Scientific, 2003: pp. 343–355. https://doi.org/10.1142/9789812705808_0027.
[6] M. Suguna, K. Saranya, A. Iampan, A Generalization of M-Bi-Ideals in b-Semirings and Its Characterizing Extension, Int. J. Anal. Appl. 22 (2024), 89. https://doi.org/10.28924/2291-8639-22-2024-89.
[7] M. Suguna, M. Palanikumar, A. Iampan, M. Geethalakshmi, New Approach towards Different Types of Bi-Quasi Ideals in b-Semirings and Its Extension, Int. J. Innov. Comput. Inf. Control 20 (2024), 75–87. https://doi.org/10.24507/ijicic.20.01.75.
[8] S.S. Chang, Salahuddin, L. Wang, Z. Ma, The Convergence Results of Differential Variational Inequality Problems, Symmetry 14 (2022), 760. https://doi.org/10.3390/sym14040760.
[9] M. Suguna, K. Saranya, A. Iampan, M.M.U. Rahman, New Approach towards Different Types of Almost Ideals in B-Semirings and Its Extension, ICIC Express Lett. 18 (2024), 1237–1245. https://doi.org/10.24507/icicel.18.12.1237.
[10] M. Henriksen, Ideals in Semigroups With Commutative Addition, Amer. Math. Soc. Notices 6 (1958), 321.
[11] K. Iséki, Quasiideals in Semirings without Zero, Proc. Japan Acad. Ser. A, Math. Sci. 34 (1958), 79–81. https://doi.org/10.3792/pja/1195524783.
[12] K. Iizuka, On the Jacobson Radical of a Semiring, Tohoku Math. J. 11 (1959), 409–421. https://doi.org/10.2748/tmj/1178244538.
[13] R.D. Jagatap, Y.S. Pawar, Quasi-Ideals and Minimal Quasi-Ideals in Semirings, Novi Sad J. Math. 39 (2009), 79–87.
[14] R.D. Jagatap, Y.S. Pawar, Bi-Ideals in Semirings, Bull. Int. Math. Virtual Inst. 6 (2016), 169–179.
[15] S. Lajos, On the Bi-Ideals in Semirings, Proc. Japan Acad. 45 (1969), 710–712.
[16] M.M.K. Rao, Tri-Ideals of Semirings, Bull. Int. Math. Virtual Inst. 10 (2020), 145–155.
[17] M. Suguna, K. Saranya, Salahuddin, Novel Investigations of m-Bi-Ideals and Generators in b-Semirings with Extended Operator Frameworks, Int. J. Anal. Appl. 22 (2024), 179. https://doi.org/10.28924/2291-8639-22-2024-179.