Unitary semi-ring on some nexuses

Authors

  • Vajiheh Nazemi Niya Department of Mathematics, Islamic Azad University of Kerman, Kerman, Iran.
  • Akbar Rezaei * Department of Mathematics, Payame Noor University, P. O. Box 19395-4697, Tehran, Iran. https://orcid.org/0000-0002-6003-3993

https://doi.org/10.48313/uda.v3i2.101

Abstract

This paper introduces and investigates a novel algebraic framework for structures composed of finite addresses, which we term nexuses. A nexus N is defined as a set of finite sequences (addresses) satisfying a closure property. We define its order, n(N), as the maximum integer value appearing among its constituent addresses. Two custom binary operations, ⊕ and ⊙n, parameterized by a natural number n, are introduced. The central construction is the generation of a semi-ring ⟨N⟩n from a given finite-order nexus N, where n = n(N). This generated structure is shown to be itself a nexus, thereby preserving the core combinatorial properties of the original set while enriching it with a coherent algebraic architecture. Notably, ⟨N⟩n is unitary, with multiplicative identity given by the unit address (1).

Keywords:

Address, Nexus, Polynomial, Semi-ring, (prime) ideal, Unitary, Homomorphism, Zero-divisor

References

  1. [1] Taba, D. A., Hasankhani, A., & Bolurian, M. (2012). Soft nexuses. Computers & mathematics with applications, 64(6), 1812-1821. https://doi.org/10.1016/j.camwa.2012.02.048
  2. [2] Bolourian, M. (2009). Theory of plenices [Thesis]
  3. [3] Bolourian, M., Kamrani, R., & Hasankhani, A. (2019). The structure of moduloid on a nexus. Mathematics, 7(1), 1-16. https://doi.org/10.3390/math7010082
  4. [4] Kamrani, R., Hasankhani, A., & Bolourian, M. (2020). Finitely generated submoduloids and prime submoduloids on a nexus. Missouri journal of mathematical sciences, 32(1), 88-109. https://doi.org/10.35834/2020/3201088
  5. [5] Kamranialiabad, R., Hasankhani, A., & Bolourian, M. (2020). On submoduloids of a moduloid on nexus. Applications and applied mathematics: An international journal (AAM), 15(2), 42. https://digitalcommons.pvamu.edu/aam/vol15/iss2/42/
  6. [6] Haristchian, M. (1980). Formex and plenix structural analysis [Thesis].
  7. [7] Hee, I. (1985). Plenix structural analysis [Thesis].
  8. [8] Hungerford, T. W.(1989). Algebra, graduate texts in mathematics, Vol. 73. Springer-Verlag, New York. https://books.google.com/books/about/Algebra.html?id=t6N_tOQhafoC
  9. [9] Niya, V. N., Babaei, H., & Rezaei, A. (2024). On fuzzy sub-semi-rings of nexuses. AIMS Mathematics, 9(12), 36140-36157. https://doi.org/10.3934/math.20241715
  10. [10] Nazemi Niya, V., Babaei, H., & Rezaei, A. (2026). On prime ideals on a semi-ring associated with a nexus. Algebraic structures and their applications, 13(3), 229-248. https://doi.org/10.22034/as.2025.23198.1796
  11. [11] Nazemi Niya, V. & Rezaei, A. (2025). Unitary semi-ring on finite nexuses [Presentation]. Proceedings of the 12th national mathematics conference of payame noor university (pp. 340–343).
  12. [12] Nooshin, H. (1984). Formex configuration processing in structural engineering. Elsevier Applied Science Publishers: London, UK. https://books.google.com/books/about/Formex_Configuration_Processing_in_Struc.html?id=e9LtAAAAIAAJ
  13. [13] Norouzi, M., Asadi, A., & Jun, Y. B. (2018). Subnexuses based on n-structures. Armenian journal of mathematics, 10(10), 1-15. https://doi.org/10.52737/18291163-2018.10.10-1-15

Downloads

Published

2026-06-25

Issue

Vol. 3 No. 2 (2026): Uncertainty Discourse and Applications

Section

Articles

How to Cite

Nazemi Niya, V., & Rezaei, A. (2026). Unitary semi-ring on some nexuses. Uncertainty Discourse and Applications, 3(2), 195-206. https://doi.org/10.48313/uda.v3i2.101

Most read articles by the same author(s)