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International Journal of Neutrosophic Science
Volume 22 , Issue 3, PP: 119-127 , 2023 | Cite this article as | XML | Html |PDF

Title

On Some n-Refined Neutrosophic Groups For 3≤ n ≤ 5

  Abuobida M. Ahmed Alfahal 1 * ,   Sara Sawalmeh 2 ,   Raja Abdullah Abdulfatah 3 ,   Yaser Ahmad Alhasan 4

1  Deanship of the Preparatory Year, Prince Sattam bin Abdulaziz University, Alkharj, Saudi Arabia
    (a.alfahal@psau.edu.sa)

2  Mutah University, Faculty of Science, Mutah, Jordan
    (Sarahsawalmeh98@gmail.com)

3  Deanship the Preparatory Year, Prince Sattam bin Abdulaziz University, Alkharj, Saudi Arabia
    (r.abdulfatah@psau.edu.sa)

4  Deanship of the Preparatory Year, Prince Sattam bin Abdulaziz University, Alkharj, Saudi Arabia
    (y.alhasan@psau.edu.sa)

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Doi   :   https://doi.org/10.54216/IJNS.220308

Received: May 06, 2023 Revised: July 10, 2023 Accepted: October 13, 2023

Abstract :

This paper is dedicated to studying some examples of n-refined neutrosophic groups and their algebraic substructures, where we deal with three different types of them, 3-refined, 4-refined, and 5-refined neutrosophic groups. Also, we present the algebraic structure of many substructures such as 3-refined neutrosophic AH-subgroups and kernels, 4-refined neutrosophic AH-homomorphisms and subgroups, and 5-refined neutrosophic AH-isomorphisms. On the other hand, many related examples will be provided to explain the algebraic concepts and their properties.

Keywords :

3-refined neutrosophic group; 4-refined neutrosophic group; 5-refined neutrosophic group.

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.

[25] Abobala, M., " n-Refined Neutrosophic Groups I", International Journal of Neutrosophic Science, Vol. 0, pp. 27-34. 2020.

Cite this Article as :
Style #
MLA Abuobida M. Ahmed Alfahal, Sara Sawalmeh, Raja Abdullah Abdulfatah, Yaser Ahmad Alhasan. "On Some n-Refined Neutrosophic Groups For 3≤ n ≤ 5." International Journal of Neutrosophic Science, Vol. 22, No. 3, 2023 ,PP. 119-127 (Doi   :  https://doi.org/10.54216/IJNS.220308)
APA Abuobida M. Ahmed Alfahal, Sara Sawalmeh, Raja Abdullah Abdulfatah, Yaser Ahmad Alhasan. (2023). On Some n-Refined Neutrosophic Groups For 3≤ n ≤ 5. Journal of International Journal of Neutrosophic Science, 22 ( 3 ), 119-127 (Doi   :  https://doi.org/10.54216/IJNS.220308)
Chicago Abuobida M. Ahmed Alfahal, Sara Sawalmeh, Raja Abdullah Abdulfatah, Yaser Ahmad Alhasan. "On Some n-Refined Neutrosophic Groups For 3≤ n ≤ 5." Journal of International Journal of Neutrosophic Science, 22 no. 3 (2023): 119-127 (Doi   :  https://doi.org/10.54216/IJNS.220308)
Harvard Abuobida M. Ahmed Alfahal, Sara Sawalmeh, Raja Abdullah Abdulfatah, Yaser Ahmad Alhasan. (2023). On Some n-Refined Neutrosophic Groups For 3≤ n ≤ 5. Journal of International Journal of Neutrosophic Science, 22 ( 3 ), 119-127 (Doi   :  https://doi.org/10.54216/IJNS.220308)
Vancouver Abuobida M. Ahmed Alfahal, Sara Sawalmeh, Raja Abdullah Abdulfatah, Yaser Ahmad Alhasan. On Some n-Refined Neutrosophic Groups For 3≤ n ≤ 5. Journal of International Journal of Neutrosophic Science, (2023); 22 ( 3 ): 119-127 (Doi   :  https://doi.org/10.54216/IJNS.220308)
IEEE Abuobida M. Ahmed Alfahal, Sara Sawalmeh, Raja Abdullah Abdulfatah, Yaser Ahmad Alhasan, On Some n-Refined Neutrosophic Groups For 3≤ n ≤ 5, Journal of International Journal of Neutrosophic Science, Vol. 22 , No. 3 , (2023) : 119-127 (Doi   :  https://doi.org/10.54216/IJNS.220308)
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