Galoitica: Journal of Mathematical Structures and Applications

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Volume 11 , Issue 2 , PP: 28-36, 2024 | Cite this article as | XML | Html | PDF | Full Length Article

On The Algebraic Classification of the 4-Cyclic Refined Neutrosophic Real Roots of Unity Group

Agnes Osagie 1

  • 1 Cape Peninsula University of Technology, Faculty of Applied Science, South Africa - (Osagieagne2000@cput.ac.za)
  • Doi: https://doi.org/10.54216/GJMSA.0110204

    Received: December 10, 2023 Revised: April 08, 2024 Accepted: July 28, 2024
    Abstract

    This paper is dedicated to finding all 4-cyclic refined neutrosophic real solutions of the equation 𝑋𝑛=1 which are called 4-cyclic refined real roots of unity. Also, we classify the algebraic group of these solutions as a direct product of some familiar finite cyclic groups. On the other hand, we illustrate many examples to clarify the validity of our work.

    Keywords :

    4-cyclic refined number , 4-cyclic neutrosophic root of unity , Abelian group , Direct product

    References

    [1] Basheer, A., Ahmad, K., and Ali, R., “A Short Contribution to Von Shtawzen's Abelian Group In n-Cyclic Refined Neutrosophic Rings", Journal Of Neutrosophic And Fuzzy Systems, 2022.

    [2] Von Shtawzen, O., “Conjectures for Invertible Diophantine Equations of 3-Cyclic and 4-Cyclic Refined Integers", Journal of Neutrosophic and Fuzzy Systems, Vol.3, 2022.

    [3] Von Shtawzen, O., “On a Novel Group Derived from a Generalization of Integer Exponents and Open Problems", Galoitica journal Of Mathematical Structures and Applications, Vol 1, 2022.

    [4] Basheer, A., Ahmad, K., and Ali, R., “On Some Open Problems about n-Cyclic Refined Neutrosophic Rings and Number Theory", Journal of Neutrosophic and Fuzzy Systems, 2022.

    [5] A. Alrida Basheer , Katy D. Ahmad , Rozina Ali., "Examples on Some Novel Diophantine Equations Derived from the Group of Units Problem in n-Cyclic Refined Neutrosophic Rings of Integers", Galoitica Journal Of Mathematical Structures And Applications, Vol.3, 2022.

    [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] 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] Sankari, H., and Abobala, M., “On the Algebraic Homomorphisms between Symbolic 2-Plithogenic Rings And 2-cyclic Refined Rings", Neutrosophic Sets and Systems, 2023.

    [9] Abobala, M., “n-Cyclic Refined Neutrosophic Algebraic Systems of Sub-Indeterminacies, an Application to Rings and Modules", International Journal of Neutrosophic Science, 2020.

    [10] Aswad, M., "n-Cyclic Refined Neutrosophic Vector Spaces and Matrices", Neutrosophic Knowledge, 2021.

    [11] Ali, R., "n-Cyclic Refined Neutrosophic Groups", International Journal of Neutrosophic Science, 2021.

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

    [13] 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.

    [14] Ahmad Salama, Rasha Dalla, Malath Al Aswad, Rozina Ali. (2022). Some Results About 2-Cyclic Refined Neutrosophic Complex Numbers. Journal of Neutrosophic and Fuzzy Systems, 4 (1), 41-8 (Doi : https://doi.org/10.54216/JNFS.040105).

    [15] Barry, W. Xu, L. Al, J. (2024). On The Diophantine 3-Cyclic Refined Neutrosophic Roots of Unity. Journal of Neutrosophic and Fuzzy Systems, 23-30. DOI: https://doi.org/10.54216/JNFS.080103

    [16] Xu, L. Sarkis, M. Rawashdeh, A. Khaldi, A. (2024). On The 4-Cyclic Refined Neutrosophic Solutions of the Diophantine Equation X^n=1 and m-Cyclic Refined Neutrosophic modulo Integers. Journal of Neutrosophic and Fuzzy Systems, (), 38-48. DOI: https://doi.org/10.54216/JNFS.080205

    Cite This Article As :
    Osagie, Agnes. On The Algebraic Classification of the 4-Cyclic Refined Neutrosophic Real Roots of Unity Group. Galoitica: Journal of Mathematical Structures and Applications, vol. , no. , 2024, pp. 28-36. DOI: https://doi.org/10.54216/GJMSA.0110204
    Osagie, A. (2024). On The Algebraic Classification of the 4-Cyclic Refined Neutrosophic Real Roots of Unity Group. Galoitica: Journal of Mathematical Structures and Applications, (), 28-36. DOI: https://doi.org/10.54216/GJMSA.0110204
    Osagie, Agnes. On The Algebraic Classification of the 4-Cyclic Refined Neutrosophic Real Roots of Unity Group. Galoitica: Journal of Mathematical Structures and Applications , no. (2024): 28-36. DOI: https://doi.org/10.54216/GJMSA.0110204
    Osagie, A. (2024) . On The Algebraic Classification of the 4-Cyclic Refined Neutrosophic Real Roots of Unity Group. Galoitica: Journal of Mathematical Structures and Applications , () , 28-36 . DOI: https://doi.org/10.54216/GJMSA.0110204
    Osagie A. [2024]. On The Algebraic Classification of the 4-Cyclic Refined Neutrosophic Real Roots of Unity Group. Galoitica: Journal of Mathematical Structures and Applications. (): 28-36. DOI: https://doi.org/10.54216/GJMSA.0110204
    Osagie, A. "On The Algebraic Classification of the 4-Cyclic Refined Neutrosophic Real Roots of Unity Group," Galoitica: Journal of Mathematical Structures and Applications, vol. , no. , pp. 28-36, 2024. DOI: https://doi.org/10.54216/GJMSA.0110204