TARU PUBLICATIONS
Journal of Interdisciplinary Mathematics cover
Open Access ·Peer-reviewed·ISSN (Online): 2169-012X·ISSN (Print): 0972-0502

Freq.: MONTHLY - Publishes the methodological and theoretical role of mathematics and mathematical applications underpinning scientific research.

Issues up to 2022 co-published with and available at:Taylor & Francis Online
submissions@tarupublications.com
Open Access Research Article

Unifying algebraic structures in mathematics for diverse theoretical applications

, * , , , , ,

* Corresponding author · click or hover a name for details

pp. 557–565Vol. 29Issue 3March 2026DOI: 10.47974/JIM-2490XML
Received:
01 Mar 2025
Published Online:
18 Mar 2026
Article type:
Research Article
Language:
EN
Article no.:
JIM-2490
Pages:
557–565

Abstract

This paper presents the way of integrating various mathematical structures into one system that will result in the improvement of academic knowledge and liberate more useful applications. The work establishes a single approach, which considers groups, rings, fields, modules, and lattices in an inclusive algebraic perspective by applying universal algebra and category theory. This can be seen as such that it is easier to map morphisms and representation theories that retain significant algebraic properties the same across structures. The proposed framework holds a great potential to improve such area as algebraic topology, cryptography, and quantum algebra through the provision of new ideas and simplification of the processes. The issues that may arise and how this unified theory can be extended in the future are also discussed. 

Keywords

Subject Classifications

06A1155N20

References

[1] J. Q. Guo, Y. J. Yin, X. L. Hu, and G. X. Ren, “Self-similar network model for fractional-order neuronal spiking: Implications of dendritic spine functions,” Nonlinear Dynamics, vol. 100, pp. 921–935 (2020).
[2] T. Y. Zhou, Y. J. Yin, G. Peng, C. Q. Luo, and Z. M. Jian, “Fractal Operators Abstracted from Arterial Blood Flow,” Fractal and Fractional, vol. 8, pp. 420 (2024).
[3] Y. Luchko, “Fractional differential equations with the general fractional derivatives of arbitrary order,” Mathematics, vol. 10, pp. 849 (2022).
[4] Y. Luchko, “Operational calculus for the general fractional derivative and its applications,” Fractional Calculus and Applied Analysis, vol. 24, pp. 338–375 (2021).
[5] V. Lebed and L. Vendramin, “On Structure Groups of Set-Theoretic Solutions to the Yang–Baxter Equation,” Proceedings of the Edinburgh Mathematical Society, vol. 62, pp. 683–717 (2019).
[6] S. K. R. Sultana, K. Sravani, N. S. Ranga Lokesh, K. Venkateswararao, and K. Lakshmaiah, “Automated ID Card Detection and Penalty System Using YOLOv5 and Face Recognition,” International Journal of Recent Advances in Engineering and Technology (IJRAET), vol. 14, no. 1, pp. 63–72 (Apr. 2025).
[7] F. Cedó, E. Jespers, and J. Okniński, “Primitive set-theoretic solutions of the Yang–Baxter equation,” Communications in Contemporary Mathematics, vol. 24, pp. 2150105 (2022).
[8] A. Smoktunowicz, “A note on set-theoretic solutions of the Yang–Baxter equation,” Journal of Algebra, vol. 500, pp. 3–18 (2018).
[9] R. K. Bandaru, A. B. Saeid, and Y. B. Jun, “On GE-algebras,” Bulletin of the Section of Logic, vol. 50, pp. 81–96 (2021).
[10] F. A. Sadiq, H. A. Ramadhan, and A. A. Aubad, “Some results on the non-zero divisor graphs of Zn,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 28, no. 4-B, pp. 1301–1307 (2025).
[11] D. Motwani, V. Chitre, V. Bhosale, M. M. Nashipudmath, S. Shinde, and A. Nerurkar, “Implementing secure elliptic curve cryptography for blockchain-based financial transactions,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 29, no. 2-A, pp. 617–627 (2026), doi: 10.47974/JDMSC-2504.
[12] S. Bhattacharya, L. Indise, N. Pandey, B. M. Nanche, S. Ramakrishna, and G. Sethi, “Analyzing the performance of wireless sensor networks using polynomial cryptography methods,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 29, no. 2-A, pp. 563–570 (2026), doi: 10.47974/JDMSC-2497.
[13] G. Kaur, M. Kaur, J. Singh, M. M. Laishram, S. Lakhanpal, and M. Kumar, “Effective strategies for writing maintainable code in cryptographic software development,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 29, no. 2-A, pp. 609–616 (2026), doi: 10.47974/JDMSC-2503.

Views: 116Downloads: 12Citations: 0