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*

mail

,

Bolivar Villalta Jadan ²

mail

,

Marcos Lalama Flores ²

mail

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

format_quote Cite this article

verified

Open Access & Copyright

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

View PDF open_in_new

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

Choose your preferred format

format_quote

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

policy

Publisher's Note

The statements, opinions, and data presented in this article are solely those of the author(s) and do not necessarily represent those of ASPG, the journal, or its editors. ASPG and the editors disclaim responsibility for any harm arising from the use of any ideas, methods, instructions, or products described in this article, to the fullest extent permitted by applicable law.

Digital Archive Ready