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

Nabil Khuder; Bolivar Villalta; Marcos Lalama

doi:https://doi.org/10.54216/IJNS.230201

Full Length Article

Volume 23 • Issue 2 • PP: 08-15 • 2024

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

Nabil Khuder Salman ^1*

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,

Bolivar Villalta Jadan ²

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,

Marcos Lalama Flores ²

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¹College Of Pharmacy, AL-Farahidi University, Baghdad, Iraq

²Universidad Regional Autónoma de los Andes (UNIANDES), Ecuador

* Corresponding Author.

DOI https://doi.org/10.54216/IJNS.230201

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

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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.

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Salman, Nabil Khuder, Jadan, Bolivar Villalta, Flores, Marcos Lalama. "On n-Refined Neutrosophic Vector Spaces For Some Special Values 3≤ n ≤6." International Journal of Neutrosophic Science, vol. Volume 23, no. Issue 2, 2024, pp. 08-15. DOI: https://doi.org/10.54216/IJNS.230201

Salman, N., Jadan, B., Flores, M. (2024). On n-Refined Neutrosophic Vector Spaces For Some Special Values 3≤ n ≤6. International Journal of Neutrosophic Science, Volume 23(Issue 2), 08-15. DOI: https://doi.org/10.54216/IJNS.230201

Salman, Nabil Khuder, Jadan, Bolivar Villalta, Flores, Marcos Lalama. "On n-Refined Neutrosophic Vector Spaces For Some Special Values 3≤ n ≤6." International Journal of Neutrosophic Science Volume 23, no. Issue 2 (2024): 08-15. DOI: https://doi.org/10.54216/IJNS.230201

Salman, N., Jadan, B., Flores, M. (2024) 'On n-Refined Neutrosophic Vector Spaces For Some Special Values 3≤ n ≤6', International Journal of Neutrosophic Science, Volume 23(Issue 2), pp. 08-15. DOI: https://doi.org/10.54216/IJNS.230201

Salman N, Jadan B, Flores M. On n-Refined Neutrosophic Vector Spaces For Some Special Values 3≤ n ≤6. International Journal of Neutrosophic Science. 2024;Volume 23(Issue 2):08-15. DOI: https://doi.org/10.54216/IJNS.230201

N. Salman, B. Jadan, M. Flores, "On n-Refined Neutrosophic Vector Spaces For Some Special Values 3≤ n ≤6," International Journal of Neutrosophic Science, vol. Volume 23, no. Issue 2, pp. 08-15, 2024. DOI: https://doi.org/10.54216/IJNS.230201

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