Submit Your Paper
  1. Home
  2. Journals
  3. International Journal of Neutrosophic Science

International Journal of Neutrosophic Science

Journal DOI

https://doi.org/10.54216/IJNS

Submit Your Paper

2690-6805ISSN (Online) 2692-6148ISSN (Print)
Submit Your Paper

Journal Menu

Homepage Journal Overview Editorial Board Submitting Articles Indexing & Abstracting

Journal Volumes

International Journal of Neutrosophic Science

Volume 25 , Issue 2 , PP: 155-164, 2025 | Cite this article as | XML | Html | PDF | Full Length Article

On the Two-Fold Maximal Units in Some Two-Fold Finite Neutrosophic Rings Modulo Integers for 2≤n≤5

Isra Al-Shbeil 1 * , Ibraheem Abu Falahah 2 , Talat Alkhouli 3 , Ahmed Soiman Rashed Alhawiti 4 , Jenan Shtayat 5 , Abdallah Al-Husban 6

  • 1 Department of Mathematics, faculty of science, University of Jordan, Amman 11942, Jordan - (i.shbeil@ju.edu.jo)
  • 2 Department of Mathematics, Faculty of Science, The Hashemite University, P.O. Box 330127, Zarqa, 13133, Jordan - (iabufalahah@hu.edu.jo)
  • 3 Applied Science Department, Aqaba University College, Balqa Applied University, Jordan - (Talat.khouli@bau.edu.jo)
  • 4 Applied Science Department, Aqaba University College, Balqa Applied University, Jordan - (ahmed.a13@tvtc.gov.sa)
  • 5 Department of mathematics, Yarmouk University, Irbid 21163, Jordan - (Jenan@inu.edu.jo)
  • 6 Department of Mathematics, Faculty of Science and Technology, Irbid National University, P.O. Box: 2600 Irbid, Jordan; Jadara Research center, Jadara University, Irbid 21110, Jordan - (dralhosban@inu.edu.jo)

    • Doi: https://doi.org/10.54216/IJNS.250213

    Received: February 11, 2024 Revised: April 29, 2024 Accepted: August 02, 2024
    Abstract

    In this paper, we have defined the concept of two-fold maximal units in finite two-fold neutrosophic rings modulo integers, where a sufficient and necessary condition for such class of generalized units will be provided. We characterize all maximal units in the following two-fold neutrosophic rings(Z_n (I))_(f_I ) for nE{2,3,4,5}.

    Keywords :

    Two-fold algebra , Finite neutrosophic ring , Modulo integer ring , minimal unit

    References

    [1]       Florentine Smarandache. "Neutrosophic Two-Fold Algebra", Plithogenic Logic and Computation, Vol.1, No.1 2024. PP.11-15.

    [2]       Mohammad Abobala. "On The Foundations of Fuzzy Number Theory and Fuzzy Diophantine Equations." Galoitica: Journal of Mathematical Structures and Applications, Vol. 10, No. 1, 2023, PP. 17-25 (Doi: https://doi.org/10.54216/GJMSA.0100102).

    [3]       Mohammad Abobala. (2023). On a Two-Fold Algebra Based on the Standard Fuzzy Number Theoretical System. Journal of Neutrosophic and Fuzzy Systems, 7 (2), 24-29. (Doi   :  https://doi.org/10.54216/JNFS.070202).

    [4]       Ahmed Hatip, Necati Olgun. (2023). On the Concepts of Two- Fold Fuzzy Vector Spaces and Algebraic Modules. Journal of Neutrosophic and Fuzzy Systems, 7 (2), 46-52. (Doi   :  https://doi.org/10.54216/JNFS.070205).

    [5]       Shihadeh, A., Matarneh, K. A. M., Hatamleh, R., Hijazeen, R. B. Y., Al-Qadri, M. O., Al-Husban, A. (2024). An Example of Two-Fold Fuzzy Algebras Based On Neutrosophic Real Numbers. Neutrosophic Sets and   Systems, 67, 169-178.‏

    [6]       [6] Sankari, H., and Abobala, M., "On the Group of Units Classification In 3-Cyclic and 4-cyclic Refined Rings of Integers and the Proof of Von Shtawzens' Conjectures", International Journal of Neutrosophic Science, 2023.

    [7]       [7] Sankari, H., and Abobala, M., “On the Classification of the Group of Units of Rational and Real 2-Cyclic Refined Neutrosophic Rings", Neutrosophic Sets and Systems, 2023.

    [8]       [8] Sadiq. B., “A Contribution To The group Of Units Problem in Some 2-Cyclic Refined Neutrosophic Rings ", International Journal of Neutrosophic Science, 2022.

    [9]       [9] Nabil Khuder Salman, Maikel Leyva Vazquez,Batista Hernández Noel. On The Classification of 3-Cyclic/4-Cyclic Refined Neutrosophic Real and Rational Von Shtawzen's Group. International Journal of Neutrosophic Science, (2024); 23 (2): 26-31.

    [10]    [10] T.Qawasmeh,R.Hatamleh,(2023).A new contraction based on H-simulation functions in the frame of extended b-metric spaces and application‏,International Journal of Electrical and Computer Engineering  13 (4),4212- 4221.

    [11]    [11] Ayman Hazaymeh, Rania Saadeh, Raed Hatamleh, Mohammad W Alomari, Ahmad Qazza,, ( 2023). A Perturbed Milne’s Quadrature Rule for n-Times Differentiable Functions with Lp-Error Estimates, Axioms-MDPI, 12(9), 803.

    [12]    [12] Katy D. Ahmad, Mikail BAL, Arwa A. Hajjari, Rozina Ali. (2021). Novel Applications of Neutrosophic AH-Isometries to the Group of Units Problem in Neutrosophic Rings and Refined Neutrosophic Rings. Journal of Neutrosophic and Fuzzy Systems, 1 (2), 89-98 (Doi   :  https://doi.org/10.54216/JNFS.010205).

    [13]    [13] Hazaymeh, Ayman, (2023). Time Effective Fuzzy Soft Set and Its Some Applications with and Without a Neutrosophic. International Journal of Neutrosophic Science 23(.2), 129-29.

    [14]    [14] Al-Husban, A., Al-Qadri, M. O., Saadeh, R., Qazza, A., & Almomani, H. H. (2022). Multi-fuzzy rings. WSEAS TRANSACTIONS on MATHEMATICS, 21, 701-706.‏

    [15]    [15] MATARNEH, K. A., AL-QADRI, M. O., AL-HUSBAN, A. B. D. A. L. L. A. H., ALDIABAT, R. I., & ALSHORM, S. (2023). Decomposition of Complete Multigraph into Wheel Graphs for Cyclic Triple System.‏ WSEAS TRANSACTIONS on MATHEMATICS. 22, 950-960.

    [16]    [16] Shihadeh, A., Matarneh, K. A. M., Hatamleh, R., Hijazeen, R. B. Y., Al-Qadri, M. O., & Al-Husban, A. (2024). An Example of Two-Fold Fuzzy Algebras Based On Neutrosophic Real Numbers. Neutrosophic Sets and Systems, 67, 169-178.‏

    [17]    [17] Abdallah Shihadeh, Khaled Ahmad Mohammad Matarneh, Raed Hatamleh, Mowafaq Omar Al-Qadri, Abdallah Al-Husban. (2024). On the Two-Fold Fuzzy n-Refined Neutrosophic Rings For 2 ≤3. Neutrosophic Sets and Systems, 68, 8-25.‏

    [18]    [18] Al-Husban, A., Salleh, A. R., & Hassan, N. (2015). Complex fuzzy normal subgroup. In AIP Conference Proceedings (Vol. 1678, No. 1). AIP Publishing.‏

    [19]    [19] Abdallah Al-Husban & Abdul Razak Salleh 2015. Complex fuzzy ring. Proceedings of 2nd International Conference on Computing, Mathematics and Statistics. Pages. 241-245. Publisher: IEEE 2015.

    [20]    [20] Abdallah Al-Husban & Abdul Razak Salleh 2015. Complex Fuzzy Hyperring Based on Complex Fuzzy Spaces. Proceedings of 2nd Innovation and Analytics Conference & Exhibition (IACE). Vol. 1691. AIP Publishing 2015. Pages 040009-040017.

    Cite This Article As :
    Al-Shbeil, Isra. , Abu, Ibraheem. , Alkhouli, Talat. , Soiman, Ahmed. , Shtayat, Jenan. , Al-Husban, Abdallah. On the Two-Fold Maximal Units in Some Two-Fold Finite Neutrosophic Rings Modulo Integers for 2≤n≤5. International Journal of Neutrosophic Science, vol. , no. , 2025, pp. 155-164. DOI: https://doi.org/10.54216/IJNS.250213
    Al-Shbeil, I. Abu, I. Alkhouli, T. Soiman, A. Shtayat, J. Al-Husban, A. (2025). On the Two-Fold Maximal Units in Some Two-Fold Finite Neutrosophic Rings Modulo Integers for 2≤n≤5. International Journal of Neutrosophic Science, (), 155-164. DOI: https://doi.org/10.54216/IJNS.250213
    Al-Shbeil, Isra. Abu, Ibraheem. Alkhouli, Talat. Soiman, Ahmed. Shtayat, Jenan. Al-Husban, Abdallah. On the Two-Fold Maximal Units in Some Two-Fold Finite Neutrosophic Rings Modulo Integers for 2≤n≤5. International Journal of Neutrosophic Science , no. (2025): 155-164. DOI: https://doi.org/10.54216/IJNS.250213
    Al-Shbeil, I. , Abu, I. , Alkhouli, T. , Soiman, A. , Shtayat, J. , Al-Husban, A. (2025) . On the Two-Fold Maximal Units in Some Two-Fold Finite Neutrosophic Rings Modulo Integers for 2≤n≤5. International Journal of Neutrosophic Science , () , 155-164 . DOI: https://doi.org/10.54216/IJNS.250213
    Al-Shbeil I. , Abu I. , Alkhouli T. , Soiman A. , Shtayat J. , Al-Husban A. [2025]. On the Two-Fold Maximal Units in Some Two-Fold Finite Neutrosophic Rings Modulo Integers for 2≤n≤5. International Journal of Neutrosophic Science. (): 155-164. DOI: https://doi.org/10.54216/IJNS.250213
    Al-Shbeil, I. Abu, I. Alkhouli, T. Soiman, A. Shtayat, J. Al-Husban, A. "On the Two-Fold Maximal Units in Some Two-Fold Finite Neutrosophic Rings Modulo Integers for 2≤n≤5," International Journal of Neutrosophic Science, vol. , no. , pp. 155-164, 2025. DOI: https://doi.org/10.54216/IJNS.250213

    Article Statistics

    View
    232
    Download
    110

    Download