On bi-bases of ordered G-semigroups
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Published
Oct 28, 2021
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Abstract
In this paper, based on the results of ordered bi-ideals generated by a non-empty subset of an ordered G-semigroups , we introduce the concept of bi-base of M. Using the quasi-order on M defined by the principal ordered bi-ideals of M. we characterize when a non-empty subset of M is a bi-base of M. The results obtained extending the results on G-semigroup.
Keywords: ordered G-Semigroup, bi-G-ideal, bi-base, quasi-order
References
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Chinnadurai, V., & Arulmozhi, K. (2018). Characterization of bipolar fuzzy ideals in ordered gamma semigroups. Journal of The International Mathematical Virtual Institute, 8, 141-156. Retrieved from https://www.imvibl.org/journal.htm
Chinram, R., & Tinpun, K. (2009). A note on minimal bi-ideals in ordered -semigroups. International Mathematical Forum, 4(1), 1-5. Retrieved from http://www.m-hikari.com/aims.html
Fabrici, I. (1975). Two-sided bases of semigroups. Matematick´y ˇCasopis, 25(2), 173-178. Retrieved from http://dml.cz/dmlcz/126947
Iampan, A. (2009).Characterizing Ordered Bi-Idealsin Ordered -Semigroups. Iranian Journal of Mathematical Sciences and Informatics, 4(1), 17-25. Retrieved from http://dx.doi.org/10.7508/
ijmsi.2009.01.002
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Kummoon, P., & Changphas, T. (2017). On bi-base of semigroup. Quasigroup and Related Systems, 25(1), 87-94. Retrieved from http://www.quasigroups.eu
Sen, M.K. (1981). On Γ-semigroups.Proceedings of International Conference on Algebra and It’s Applications, New York, 301-308.
Sen, M. K., & Saha, N. K. (1986). On Γ-semigroup I. Bulletin of Calcutta Mathematical Society, 78, 180-186.
Saha, N. K. (1987). On Γ-semigroup II. Bulletin of Calcutta Mathematical Society, 79, 331-335.
Saha, N. K. (1998). On Γ-semigroup III. Bulletin of Calcutta Mathematical Society, 80, 1-13.
Chinnadurai, V., & Arulmozhi, K. (2018). Characterization of bipolar fuzzy ideals in ordered gamma semigroups. Journal of The International Mathematical Virtual Institute, 8, 141-156. Retrieved from https://www.imvibl.org/journal.htm
Chinram, R., & Tinpun, K. (2009). A note on minimal bi-ideals in ordered -semigroups. International Mathematical Forum, 4(1), 1-5. Retrieved from http://www.m-hikari.com/aims.html
Fabrici, I. (1975). Two-sided bases of semigroups. Matematick´y ˇCasopis, 25(2), 173-178. Retrieved from http://dml.cz/dmlcz/126947
Iampan, A. (2009).Characterizing Ordered Bi-Idealsin Ordered -Semigroups. Iranian Journal of Mathematical Sciences and Informatics, 4(1), 17-25. Retrieved from http://dx.doi.org/10.7508/
ijmsi.2009.01.002
Kehayopulu, N. (2010), On ordered -semigroups. Scientiae Mathematicae Japonicae, 23, 37-43.
Kummoon, P., & Changphas, T. (2017). Bi-Bases of -semigroup. Thai Journal of Mathematics, 75-86. Retrieved from http://thaijmath.in.cmu.ac.th
Kummoon, P., & Changphas, T. (2017). On bi-base of semigroup. Quasigroup and Related Systems, 25(1), 87-94. Retrieved from http://www.quasigroups.eu
Sen, M.K. (1981). On Γ-semigroups.Proceedings of International Conference on Algebra and It’s Applications, New York, 301-308.
Sen, M. K., & Saha, N. K. (1986). On Γ-semigroup I. Bulletin of Calcutta Mathematical Society, 78, 180-186.
Saha, N. K. (1987). On Γ-semigroup II. Bulletin of Calcutta Mathematical Society, 79, 331-335.
Saha, N. K. (1998). On Γ-semigroup III. Bulletin of Calcutta Mathematical Society, 80, 1-13.
Section
Research Articles
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How to Cite
JANTANAN, Wichayaporn; LATTHI, Monthean; PUIFAI, Jiriya.
On bi-bases of ordered G-semigroups.
Naresuan University Journal: Science and Technology (NUJST), [S.l.], v. 30, n. 3, p. 75-84, oct. 2021.
ISSN 2539-553X.
Available at: <https://www.journal.nu.ac.th/NUJST/article/view/Vol-30-No-3-2022-75-84>. Date accessed: 26 apr. 2024.
doi: https://doi.org/10.14456/nujst.2022.28.