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International Journal of Neutrosophic Science

Volume 12 , Issue 2 , PP: 81-95, 2020 | Cite this article as | XML | Html | PDF | Full Length Article

n-Cyclic Refined Neutrosophic Algebraic Systems of Sub-Indeterminacies, An Application to Rings and Modules

Mohammad Abobala 1

  • 1 Faculty of Science, Tishreen University, Lattakia, Syria - (mohammadabobala777@gmail.com)

    • Doi: https://doi.org/10.54216/IJNS.120203

    Received: July 08, 2020 Accepted: November 12, 2020
    Abstract

     

    Refining the indeterminate I into many levels of indeterminacy is a way to explore many neutrosophic algebraic structures.This paper introduces the concept of n-cyclic refined algebraic system of sub-indeterminacies as a new way to refine a neutrosophic indeterminate I. This idea will be used to introduce the notion of n-cyclic refined neutrosophic ring and to study its AH-substructures. Also, this work presents the concept of n-cyclic refined neutrosophic modules with many related structures.

     

    Keywords :

      ,

    n-cyclic refined neutrosophic system, n-cyclic refined neutrosophic ring, n-cyclic refined neutrosophic AH-substructures, n-cyclic refined neutrosophic modules, n-cyclic refined neutrosophic homomorphisms.

      ,

    References

     

    [1]  Abobala, M., "AH-Subspaces in Neutrosophic Vector Spaces", International Journal of Neutrosophic Science, Vol. 6 , pp. 80-86, 2020.

     

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

     

    [3]  Abobala, M,. "Classical Homomorphisms Between Refined Neutrosophic Rings and Neutrosophic Rings", International Journal of Neutrosophic Science, Vol. 5, pp. 72-75, 2020.

     

    [4]  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.

     

    [5]  Abobala, M., "On Some Special Substructures of Neutrosophic Rings and Their Properties", International Journal of Neutrosophic Science", Vol. 4 , pp. 72-81, 2020.

     

    [6]  Abobala, M., "On Some Special Substructures of Refined Neutrosophic Rings", International Journal of     Neutrosophic Science, Vol. 5, pp. 59-66, 2020.

     

    [7]  Alhamido, R., and Gharibah, T., "Neutrosophic Crisp Tri-Topological Spaces", Journal of New Theory, Vol. 23 , pp.13-21, 2018.

     

    [8]  Alhamido, R., and Abobala, M., "AH-Substructures in Neutrosophic Modules", International Journal of Neutrosophic Science, Vol. 7, pp. 79-86 , 2020.

     

    [9]  Agboola, A.A.A,. and Akinleye, S.A,. "Neutrosophic Vector Spaces", Neutrosophic Sets and Systems, Vol. 4 , pp. 9-17, 2014.

     

    [10]   Agboola, A.A.A., “On Reļ¬ned Neutrosophic Algebraic Structures”, Neutrosophic Sets and Systems,Vol.10, pp. 99-101, 2015.

     

    [11]   Anjrou, S., "Linear Algebra 1", Tishreen University Press, pp. 121-205, 2018.

     

    [12]  Hatip, A., and Olgun, N., " On Refined Neutrosophic R-Module", International Journal of Neutrosophic Science, Vol. 7, pp.87-96, 2020.

     

    [13]    Hatip, A., Alhamido, R., and Abobala, M., "A Contribution to Neutrosophic Groups", International Journal of Neutrosophic Science", Vol. 0, pp. 67-76 , 2019.

     

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

     

    [15] 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.

     

    [16]     Ibrahim, M.A., Agboola, A.A.A, Badmus, B.S., and Akinleye, S.A., "On Refined Neutrosophic Vector Spaces II", International Journal of Neutrosophic Science, Vol. 9, pp. 22-36, 2020.

     

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

     

    [18]  Smarandache, F., and Abobala, M., "n-Refined neutrosophic Rings", International Journal of Neutrosophic Science, Vol. 5, pp. 83-90, 2020.

     

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

     

    [20]   F. Smarandache, Refined Literal Indeterminacy and the Multiplication Law of Subindeterminacies, Chapter 5, pp. 133-160, in the book by the same author, Symbolic Neutrosophic Theory, EuropaNova asbl Bruxelles, 2015, http://fs.unm.edu/SymbolicNeutrosophicTheory.pdf

     

    Cite This Article As :
    Abobala, Mohammad. n-Cyclic Refined Neutrosophic Algebraic Systems of Sub-Indeterminacies, An Application to Rings and Modules. International Journal of Neutrosophic Science, vol. , no. , 2020, pp. 81-95. DOI: https://doi.org/10.54216/IJNS.120203
    Abobala, M. (2020). n-Cyclic Refined Neutrosophic Algebraic Systems of Sub-Indeterminacies, An Application to Rings and Modules. International Journal of Neutrosophic Science, (), 81-95. DOI: https://doi.org/10.54216/IJNS.120203
    Abobala, Mohammad. n-Cyclic Refined Neutrosophic Algebraic Systems of Sub-Indeterminacies, An Application to Rings and Modules. International Journal of Neutrosophic Science , no. (2020): 81-95. DOI: https://doi.org/10.54216/IJNS.120203
    Abobala, M. (2020) . n-Cyclic Refined Neutrosophic Algebraic Systems of Sub-Indeterminacies, An Application to Rings and Modules. International Journal of Neutrosophic Science , () , 81-95 . DOI: https://doi.org/10.54216/IJNS.120203
    Abobala M. [2020]. n-Cyclic Refined Neutrosophic Algebraic Systems of Sub-Indeterminacies, An Application to Rings and Modules. International Journal of Neutrosophic Science. (): 81-95. DOI: https://doi.org/10.54216/IJNS.120203
    Abobala, M. "n-Cyclic Refined Neutrosophic Algebraic Systems of Sub-Indeterminacies, An Application to Rings and Modules," International Journal of Neutrosophic Science, vol. , no. , pp. 81-95, 2020. DOI: https://doi.org/10.54216/IJNS.120203

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