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International Journal of Neutrosophic Science

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International Journal of Neutrosophic Science

Volume 18 , Issue 4 , PP: 08-15, 2022 | Cite this article as | XML | Html | PDF | Full Length Article

On the Classification of n-Refined Neutrosophic Rings and Its Applications in Matrix Computing Algorithms and Linear Systems

Katy D. Ahmad 1 * , N.N.Thjeel 2 , M.M. Abdul Zahra 3 , R.A. Jaleel 4

  • 1 Islamic University Of Gaza, Palestine - (katyon765@gmail.com)
  • 2 Thi-Qar University, Thi-Qar, Iraq - (nna90619@gmail.com)
  • 3 Computer Techniques Department, Al-Mustaqbal University College, Hillah, Iraq - (musaddaqmahir@mustaqbal-college.edu.iq)
  • 4 Department of Information and Communication Engineering, Al-Nahrain University, Baghdad, Iraq - (iraqit2010@yahoo.com)

    • Doi: https://doi.org/10.54216/IJNS.180401

    Received: February 23, 2022 Accepted: June 15, 2022
    Abstract

    This work is dedicated to classifying the general n-refined neutrosophic ring by building a ring isomorphism and the direct product of the corresponding classical rings with itself. On the other hand, we use the classification property to solve the problem of n-refined neutrosophic computing of Eigen values and Eigen vectors of an n-refined neutrosophic matrix. Also, it will be applied to solve n-refined linear systems and models.

    Keywords :

    n-refined neutrosophic ring , n-refined neutrosophic matrix , neutrosophic eigen value , neutrosophic eigen vector.

    References

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    [2] M. Abobala. n-Cyclic Refined Neutrosophic Algebraic Systems Of Sub-Indeterminacies, An

    Application To Rings and Modules, International Journal of Neutrosophic Science, Vol. 12, 2020. pp.

    81-95 .

    [3] Olgun, N., Hatip, A., Bal, M., and Abobala, M., " A Novel Approach To Necessary and Sufficient

    Conditions For The Diagonalization of Refined Neutrosophic Matrices", International Journal of

    Neutrosophic Science, Vol. 16, pp. 72-79, 2021.

    [4] E. Adeleke. A. Agboola. , and F. Smarandache. Refined Neutrosophic Rings II. IJNS, 2020.

    [5] Ibrahim, M., and Abobala, M., "An Introduction To Refined Neutrosophic Number Theory",

    Neutrosophic Sets and Systems, Vol. 45, 2021.

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    2020.

    [10] Chalapathi, T., and Madhavi, L., "Neutrosophic Boolean Rings", NSS, Vol. 33, pp. 57-66. 2020.

    [11] Smarandache, F., " n-Valued Refined Neutrosophic Logic and Its Applications in Physics", Progress in

    Physics, 143-146, Vol. 4, 2013.

    [12] Abobala, M., Hatip, A., Bal,M.," A Study Of Some Neutrosophic Clean Rings", International journal of

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    [13] F. Smarandache, Introduction to Neutrosophic Statistics, USA: Sitech & Education Publishing, 2014.

    [14] Bal, M., Ahmad, K., Hajjari, A., Ali, R.," The Structure Of Imperfect Triplets In Several Refined

    Neutrosophic Rings" Journal of Neutrosophic and Fuzzy Systems, 2022.

    [15] Ceven, Y., and Tekin, S., " Some Properties of Neutrosophic Integers", Kırklareli University Journal of

    Engineering and Science, Vol. 6, pp.50-59, 2020.

    [16] Abobala, M., "On Some Algebraic Properties of n-Refined Neutrosophic Elements and n-Refined

    Neutrosophic Linear Equations", Mathematical Problems in Engineering, Hindawi, 2021

    [17] Abobala, M., Bal, M., and Hatip, A.," A Review On Recent Advantages In Algebraic Theory Of

    Neutrosophic Matrices", International Journal of Neutrosophic Science, Vol. 17, 2021.

    [18] M. Ali, F. Smarandache, M. Shabir and L. Vladareanu., "Generalization of Neutrosophic Rings and

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    Cite This Article As :
    D., Katy. , , N.N.Thjeel. , Abdul, M.M.. , Jaleel, R.A.. On the Classification of n-Refined Neutrosophic Rings and Its Applications in Matrix Computing Algorithms and Linear Systems. International Journal of Neutrosophic Science, vol. , no. , 2022, pp. 08-15. DOI: https://doi.org/10.54216/IJNS.180401
    D., K. , N. Abdul, M. Jaleel, R. (2022). On the Classification of n-Refined Neutrosophic Rings and Its Applications in Matrix Computing Algorithms and Linear Systems. International Journal of Neutrosophic Science, (), 08-15. DOI: https://doi.org/10.54216/IJNS.180401
    D., Katy. , N.N.Thjeel. Abdul, M.M.. Jaleel, R.A.. On the Classification of n-Refined Neutrosophic Rings and Its Applications in Matrix Computing Algorithms and Linear Systems. International Journal of Neutrosophic Science , no. (2022): 08-15. DOI: https://doi.org/10.54216/IJNS.180401
    D., K. , , N. , Abdul, M. , Jaleel, R. (2022) . On the Classification of n-Refined Neutrosophic Rings and Its Applications in Matrix Computing Algorithms and Linear Systems. International Journal of Neutrosophic Science , () , 08-15 . DOI: https://doi.org/10.54216/IJNS.180401
    D. K. , N. , Abdul M. , Jaleel R. [2022]. On the Classification of n-Refined Neutrosophic Rings and Its Applications in Matrix Computing Algorithms and Linear Systems. International Journal of Neutrosophic Science. (): 08-15. DOI: https://doi.org/10.54216/IJNS.180401
    D., K. , N. Abdul, M. 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, vol. , no. , pp. 08-15, 2022. DOI: https://doi.org/10.54216/IJNS.180401

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