Intersection properties applicable for tri quasi-ideals of an ordered (η1, η2)-regular semigroups
Keywords:
Ordered semigroups, quasi ideals, tri quasi ideals, (η1,η2)-tri quasi ideals.Abstract
The purpose of this work is to study ordered (η1,η2)-regular semirings according to the properties of their ordered various ideals. We focus on ordered semigroups, where an index η1 and η2 characterize the tri quasi ideals and (η1,η2)-tri quasi ideals. We also talk about some important ways in which these principles interact. The (η1,η2)-intersection property of each (η1,η2)-tri quasi-ideal and the (η1,η2)-quasi ideals of (η1, η2)-regular ordered semigroups define these semigroups. The (η1,η2)-tri quasi-ideal is the intersection of a η1-left tri quasi-ideal and a η2-right tri-ideal.
References
[1] Gan, A. P., & Jiang, Y. L. (2011). On ordered ideals in ordered semirings. Journal of Mathematical Research and Exposition, 31(6), 989–996.
[2] Mandal, D. (2014). Fuzzy ideals and fuzzy interior ideals in ordered semirings. Fuzzy Information and Engineering, 6(1), 101–114.
[3] Almeida, J.; Margolis, S.; Steinberg, B.; Volkov, M. Representation theory of finite semigroups, semigroup radicals and formal language theory. Trans. Am. Math. Soc. 2009, 361, 1429–1461.
[4] Lallement, G. Semigroups and Combinatorial Applications; John Wiley & Sons Inc.: Hoboken, NJ, USA, 1979.
[5] M. Munir, and A. Shafiq. A generalization of bi ideals in semirings. Bull. Int. Math. Virt. Inst, 8(1)(2018), 123–133.
[6] M. Munir. On m-bi ideals in semigroups. Bull. Int. Math. Virt. Inst. 8(3)(2018), 461–467.
[7] Kehayopulu, N. On completely regular ordered semigroups. Sci. Math. 1998, 1, 27–32.
[8] Kehayopulu, N.; Tsingelis, M. On left regular ordered semigroups. Southeast Asian Bull. Math. 2002, 25, 609–615.
[9] V.Ramya. (2025). Selective Learning Activation Strategies for Scalable Autonomous Distributed Systems. SECITS Journal of Scalable Distributed Computing and Pipeline Automation, 2(2), 38–44.
[10] Lee, S.K.; Lee, S.S. Left(right)-filters on po-semigroups. Kangweon-Kyungki Math. J. 2000, 8, 43–45.
[11] J. Ahsan, M. Takahashi, Pure spectrum of a monoid with zero, Kobe J. Mathematics, 6(1989), 163–182
[12] Nidhi Mishra, & Ashu Nayak. (2026). Engineering Multi-Agent Simulation Systems for Conflict and Cooperation Modelling: A Systems Dynamics Perspective. Advances in Mechanical Engineering and Applications, 2(1), 1–9.
[13] S. Bashir, M. Shabir, Pure ideals in ternary semigroups, Quasigroups and Related Systems, 17(2009), 149–160.
[14] Moti Ranjan Tandi, & M. Sathish Kumar. (2025). Quantum-Inspired Reconfigurable Computing for Accelerated Matrix Computations in High-Performance Embedded Systems. SCCTS Journal of Embedded Systems Design and Applications, 3(2), 48–58.
[15] M. Palanikumar, K. Arulmozhi, C. Jana, M. Pal, K.P. Shum, New approach towards different bi-base of ordered b-semiring, Asian-European Journal of Mathematics, 16(02), 2350019.
[16] Rajan.C, & N. Saranya. (2025). Nonlinear Dynamical Modeling and Control Strategies for Vibration Mitigation in Smart Structural Systems. Journal of Applied Mathematical Models in Engineering, 1(2), 32–39.
[17] M. Palanikumar, K. Arulmozhi, Aiyared Iampan, L. J. Manavalan, Different approach towards ordered almost ideals of ordered semirings, ICIC Express Letters Part B: Applications ICIC International, 13(12), 2022.
[18] T.M. Sathish Kumar, & Shaik Sadulla. (2025). Fractional-Order Mathematical Models for Vibration Analysis in Smart Structural Systems. Journal of Applied Mathematical Models in Engineering, 1(4), 1–8.
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