Pairs of soft ideals in a ternary semigroup
*Panuwat LuangchaisriCorresponding authorpanulu@kku.ac.thDepartment of MathematicsFaculty of ScienceKhon Kaen UniversityKhon Kaen, 40002, ThailandView full profile → , Thawhat Changphasthacha@kku.ac.thDepartment of MathematicsFaculty of ScienceKhon Kaen UniversityKhon Kaen, 40002, ThailandView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 02 Oct 2023
- Published Online:
- 17 Jul 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JDMSC-2141
- Pages:
- 2589–2598
Abstract
The purpose of this paper is to introduce the concept of a pair soft left (resp. right, lateral) ideal of a ternary semigroup. Relationships between a pair soft left (resp. right, lateral) ideal, a soft left (resp. right, lateral) ideal, and a regular (quasi-regular) semigroup are described.
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References
[1] M. Y. Abbasi, S. A. Khan, and A. Ali, “A note on soft ideals and soft filters in ternary semigroups with involution,” Discussiones Mathematicae, General Algebra and Applications, vol. 40, pp. 119–133 (2020).
[2] U. Acar, F. Koyuncu, and B. Tanay, “Soft sets and soft rings,” Computers & Mathematics with Applications, vol. 59, pp. 3458–3463 (2010).
[3] H. Aktaş and N. Çağman, “Soft sets and soft groups,” Information Sciences, vol. 177, pp. 2726–2735 (2007).
[4] M. I. Ali, M. Shabir, and K. P. Shum, “On soft ideals over semigroups,” Southeast Asian Bulletin of Mathematics, vol. 34, pp. 595–610 (2010).
[5] M. I. Ali, “Soft ideals and soft filters of soft ordered ternary semigroups,” Computers & Mathematics with Applications, vol. 62, pp. 3396–3403 (2011).
[6] M. I. Ali, F. Feng, X. Y. Liu, W. K. Min, and M. Shabir, “On some new operations in soft set theory,” Computers & Mathematics with Applications, vol. 57, pp. 1547–1553 (2009).
[7] T. Changphas and B. Thongkam, “On soft algebras in a general viewpoint,” International Journal of Algebra, vol. 6, pp. 109–116 (2012).
[8] A. Chronowski, “Congruences on ternary semigroups,” Ukrainian Mathematical Journal, vol. 56, pp. 662–681 (2004).
[9] A. Chronowski, “A ternary semigroup of mappings,” Demonstratio Mathematica, vol. 27, pp. 781–791 (1994).
[10] A. Chronowski, “On ternary semigroups of lattice homomorphisms,” Quasigroups and Related Systems, vol. 3, pp. 55–72 (1996).
[11] V. N. Dixit and S. Dewan, “A note on quasi and bi-ideals in ternary semigroups,” International Journal of Mathematics and Mathematical Sciences, vol. 18, pp. 501–508 (1995).
[12] F. Feng, X. Y. Liu, V. Leoreanu-Fotea, and Y. B. Jun, “Soft sets and soft rough sets,” Information Sciences, vol. 181, pp. 1125–1137 (2011).
[13] F. Feng, Y. B. Jun, and X. Zhao, “Soft semirings,” Computers & Mathematics with Applications, vol. 56, pp. 2621–2628 (2008).
[14] S. Kar and I. Dutta, “Soft ideals of soft ternary semigroups,” Heliyon, vol. 7, pp. 1–8 (2021).
[15] D. Molodtsov, “Soft set theory—first results,” Computers & Mathematics with Applications, vol. 37, pp. 19–31 (1999).
[16] M. Shabir and M. I. Ali, “Soft ideals and generalized fuzzy ideals in semigroups,” New Mathematics and Natural Computation, vol. 5, pp. 599–615 (2009).
[17] M. Shabir and M. Bano, “Prime bi-ideals in ternary semigroups,” Quasigroups and Related Systems, vol. 16, pp. 239–256 (2008).
[18] M. Shabir and A. Ali, “On soft ternary semigroups,” Annals of Fuzzy Mathematics and Informatics, vol. 3, pp. 39–59 (2012).
[19] F. M. Sioson, “Ideal theory in ternary semigroups,” Mathematica Japonica, vol. 10, pp. 63–84 (1965).
[20] A. F. Talee, M. Y. Abbasi, K. Hila, and S. A. Khan, “A new approach towards int-soft hyperideals in ordered ternary semihypergroups,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 25, pp. 1239–1259 (2022).
[21] A. F. Talee, M. Y. Abbasi, S. A. Khan, and K. Hila, “Fuzzy set approach to hyperideal theory of po-ternary semihypergroups,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 22, pp. 411–431 (2019).




