Prime Bi-Ideals in Ordered Ternary Semigroups

Article Sidebar

PDF
DOI: https://doi.org/10.28924/2291-8639-24-2026-292
Published: Sep 21, 2026
Cite as:
Jatuporn Sanborisoot, Prime Bi-Ideals in Ordered Ternary Semigroups, Int. J. Anal. Appl., 24 (2026), 292.

Main Article Content

Jatuporn Sanborisoot

Abstract

In this work, we introduce the concepts of prime, semiprime, strongly prime irreducible, and strongly irreducible bi-ideals of ordered ternary semigroups. We characterize those ordered ternary semigroups for which every bi-ideal is strongly prime. We also prove that the space of all strongly prime bi-ideals forms a topological space.

Article Details

References

  1. T. Changphas, Bi-Ideals in Ordered Ternary Semigroups, Appl. Math. Sci. 6 (2012), 5943-5946.
  2. V.R. Daddi, Y.S. Pawar, On Ordered Ternary Semigroups, Kyungpook Math. J. 52 (2012), 375-381. https://doi.org/10.5666/KMJ.2012.52.4.375.
  3. V.N. Dixit, S. Dewan, A Note on Quasi and Bi-Ideals in Ternary Semigroups, Int. J. Math. Math. Sci. 18 (1995), 501-508. https://doi.org/10.1155/s0161171295000640.
  4. V.N. Dixit, S. Dewan, Minimal Quasi-Ideals in Ternary Semigroups, Indian J. Pure Appl. Math. 28 (1997), 625-632.
  5. T.K. Dutta, S. Kar, On Semiprime Ideals and Irreducible Ideals of Ternary Semiring, Bull. Cal. Math. Soc. 97 (2005), 467-476.
  6. T.K. Dutta, S. Kar, On Prime Ideals and Prime Radical of Ternary Semiring, Bull. Cal. Math. Soc. 97 (2005), 445-454.
  7. J.M. Howie, Fundamentals of Semigroup Theory, Oxford University Press, New York, 1995.
  8. A. Iampan, Characterizing the Minimality and Maximality of Ordered Lateral Ideals in Ordered Ternary Semigroups, J. Korean Math. Soc. 46 (2009), 775-784. https://doi.org/10.4134/JKMS.2009.46.4.775.
  9. A. Iampan, On Ordered Ideal Extensions of Ordered Ternary Semigroups, Lobachevskii J. Math. 31 (2010), 13-17. https://doi.org/10.1134/s1995080210010038.
  10. P. Jailoka, A. Iampan, Minimality and Maximality of Ordered Quasi-Ideals in Ordered Ternary Semigroups, Gen. Math. Notes, 21 (2014), 42-58.
  11. D.H. Lehmer, A Ternary Analogue of Abelian Groups, American Journal of Mathematics. 54 (1932), 329-338. https://doi.org/10.2307/2370997.
  12. J. Los, On the Extending of Models (I), Fundam. Math. 42 (1955), 38-54. https://eudml.org/doc/213372.
  13. J. Sanborisoot, T. Changphas, On Pure Ideals in Ordered Ternary Semigroups, Thai J. Math. 12 (2014), 455-464.
  14. M. Shabir, N. Kanwal, Prime Bi-Ideals of Semigroups, Southeast Asian Bull. Math. 31 (2007), 757-764.
  15. M. Shabir, M. Bano, Prime Bi-Ideals in Ternary Semigroups, Quasigroups Related Syst. 16 (2008), 239-256.
  16. F.M. Sioson, Ideal Theory in Ternary Semigroups, Math. Japonica. 10 (1965), 63-84.
  17. B. Thongkam, T. Changphas, On One-Sided Bases of a Ternary Semigroup, Int. J. Pure Appl. Math. 103 (2015), 429-437. https://doi.org/10.12732/ijpam.v103i3.5.