International Journal of Neutrosophic Science

Journal DOI

https://doi.org/10.54216/IJNS

Submit Your Paper

2690-6805ISSN (Online) 2692-6148ISSN (Print)

Volume 23 , Issue 2 , PP: 08-15, 2024 | Cite this article as | XML | Html | PDF | Full Length Article

On n-Refined Neutrosophic Vector Spaces For Some Special Values 3≤ n ≤6

Nabil Khuder Salman 1 * , Bolívar Villalta Jadan 2 , Marcos Lalama Flores 3

  • 1 College Of Pharmacy, AL-Farahidi University, Baghdad, Iraq - (nsalman@uoalfarahidi.edu.iq)
  • 2 Universidad Regional Autónoma de los Andes (UNIANDES), Ecuador - (us.bolivarvillalta@uniandes.edu.ec)
  • 3 Universidad Regional Autónoma de los Andes (UNIANDES), Ecuador - (u ua.marcoslalama@uniandes.edu.ec)
  • Doi: https://doi.org/10.54216/IJNS.230201

    Received: May 22, 2023 Revised: October 12, 2023 Accepted: November 08, 2023
    Abstract

    This work is dedicated to study some different types of n-refined neutrosophic vector spaces for different values of n between 3 and 6. Where we present some related algebraic concepts such as 3-refined neutrosophic homomorphism, 4-refined neutrosophic homomorphism, 5-refined neutrosophic homomorphism, and 6-refined neutrosophic homomorphism. Also, we provide some theorems to clarify the algebraic behaviour of 3-refined, 4-refined, 5-refined, and 6-refined neutrosophic subspaces.

    Keywords :

    3-refined neutrosophic vector space , 4-refined neutrosophic vector space , 5-refined neutrosophic vector space , 6-refined neutrosophic vector space , n-refined homomorphism.

    References

    [1] Agboola, A.A.A,. Akwu, A.D,. and Oyebo, Y.T,. "Neutrosophic Groups and Subgroups", International .J .Math.Combin, Vol. 3, pp. 1-9, 2012.

    [2] Agboola, A.A.A., Akinola, A.D., and Oyebola, O.Y.," NeutrosophicRings I ", International J.Mathcombin, Vol. 4, pp. 1-14, 2011.

    [3] Agboola, A.A.A., "On Refined Neutrosophic Algebraic Structures", Neutrosophic Sets and Systems, Vol. 10, pp. 99-102, 2015.

    [4] Abobala, M., On Refined Neutrosophic Matrices and Their Applications In Refined Neutrosophic Algebraic Equations, Journal Of Mathematics, Hindawi, 2021

    [5] Merkepci, H., and Ahmad, K., " On The Conditions Of Imperfect Neutrosophic Duplets and Imperfect Neutrosophic Triplets", Galoitica Journal Of Mathematical Structures And Applications, Vol.2, 2022.

    [6] Abobala, M., Hatip, A., Olgun, N., Broumi, S., Salama, A,A., and Khaled, E, H., The algebraic creativity In The Neutrosophic Square Matrices, Neutrosophic Sets and Systems, Vol. 40, pp. 1-11, 2021.

    [7] Hatip, A., and Abobala, M., "AH-Substructures In Strong Refined Neutrosophic Modules", International Journal of Neutrosophic Science, Vol. 9, pp. 110-116 . 2020.

    [8] Kandasamy, V.W.B., and Smarandache, F., "Some Neutrosophic Algebraic Structures and Neutrosophic N-Algebraic Structures", Hexis, Phonex, Arizona 2006.

    [9] Smarandache, F., "Symbolic Neutrosophic Theory", EuropaNova asbl, Bruxelles, 2015.

    [10] Smarandache, F., "n-Valued Refined Neutrosophic Logic and Its Applications in Physics", Progress in Physics, Vol. 4, pp.143-146, 2013.

    [11] Abobala, M., and Hatip, A., " An Algebraic Approach To Neutrosophic Euclidean Geometry", Neutrosophic Sets and Systems, 2021.

    [12] Abobala, M., "On The Characterization of Maximal and Minimal Ideals In Several Neutrosophic Rings", Neutrosophic Sets and Systems, Vol. 45, 2021.

    [13] Abobala, M., "Neutrosophic Real Inner Product Spaces", Neutrosophic Sets and Systems, Vol. 43, 2021

    [14] Sarkis, M., " On The Solutions Of Fermat's Diophantine Equation In 3-refined Neutrosophic Ring of Integers", Neoma Journal of Mathematics and Computer Science, 2023.

    [15] Smarandache, F., and Abobala, M., "n-Refined Neutrosophic Rings", International Journal Of Neutrosophic Science, 2020.

    [16] Ahmad, K., Thjeel, N., AbdulZahra, M., and Jaleel, R., " On The Classification of n-Refined Neutrosophic Rings And Its Applications In Matrix Computing Algorithms And Linear Systems", International Journal Of Neutrosophic Science, 2022.

    [17] Celik, M., and Hatip, A., " On The Refined AH-Isometry And Its Applications In Refined Neutrosophic Surfaces", Galoitica Journal Of Mathematical Structures And Applications, 2022.

    [18] Abobala, M., "On Some Algebraic Properties of n-Refined Neutrosophic Elements and n-Refined Neutrosophic Linear Equations", Mathematical Problems in Engineering, Hindawi, 2021.

    [19] Adeleke, E.O., Agboola, A.A.A., and Smarandache, F., "Refined Neutrosophic Rings II", International Journal of Neutrosophic Science, Vol. 2(2), pp. 89-94. 2020.

    [20] Ibrahim, M.A., Agboola, A.A.A, Badmus, B.S. and Akinleye, S.A., "On refined Neutrosophic Vector Spaces I", International Journal of Neutrosophic Science, Vol. 7, pp. 97-109. 2020.

    [21] Al Aswad, M., and Dalla, R., " Neutrosophic Divisor Point of  A Straight Line Segment With A Given Ratio", Pure Mathematics for Theoretical Computer Science, Vol.2, 2023.

    [22] Smarandache F., and Abobala, M.,  "n-Refined Neutrosophic Vector Spaces", International Journal of Neutrosophic Science, Vol. 7, pp. 47-54. 2020.

    [23] Sankari, H., and Abobala, M." n-Refined Neutrosophic Modules", Neutrosophic Sets and Systems, Vol. 36, pp. 1-11. 2020.

    [24] Abobala, M.,. "A Study of AH-Substructures in n-Refined Neutrosophic Vector Spaces", International Journal of Neutrosophic Science", Vol. 9, pp.74-85. 2020.

     

     

     

     

     

    Cite This Article As :
    Khuder, Nabil. , Villalta, Bolívar. , Lalama, Marcos. On n-Refined Neutrosophic Vector Spaces For Some Special Values 3≤ n ≤6. Journal of International Journal of Neutrosophic Science, vol. 23, no. 2, 2024, pp. 08-15. DOI: https://doi.org/10.54216/IJNS.230201
    Khuder, N. Villalta, B. Lalama, M. (2024). On n-Refined Neutrosophic Vector Spaces For Some Special Values 3≤ n ≤6. Journal of International Journal of Neutrosophic Science, 23( 2), 08-15. DOI: https://doi.org/10.54216/IJNS.230201
    Khuder, Nabil. Villalta, Bolívar. Lalama, Marcos. On n-Refined Neutrosophic Vector Spaces For Some Special Values 3≤ n ≤6. Journal of International Journal of Neutrosophic Science 23, no. 2 (2024): 08-15. DOI: https://doi.org/10.54216/IJNS.230201
    Khuder, N. , Villalta, B. , Lalama, M. (2024) . On n-Refined Neutrosophic Vector Spaces For Some Special Values 3≤ n ≤6. Journal of International Journal of Neutrosophic Science , 23( 2) , 08-15 . DOI: https://doi.org/10.54216/IJNS.230201
    Khuder N. , Villalta B. , Lalama M. [2024]. On n-Refined Neutrosophic Vector Spaces For Some Special Values 3≤ n ≤6. Journal of International Journal of Neutrosophic Science. 23( 2): 08-15. DOI: https://doi.org/10.54216/IJNS.230201
    Khuder, N. Villalta, B. Lalama, M. "On n-Refined Neutrosophic Vector Spaces For Some Special Values 3≤ n ≤6," Journal of International Journal of Neutrosophic Science, vol. 23, no. 2, pp. 08-15, 2024. DOI: https://doi.org/10.54216/IJNS.230201