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

Mohammad

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

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Volume 12 • Issue 2 • PP: 81-95 • 2020

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

Mohammad Abobala ^1*

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¹Faculty of Science, Tishreen University, Lattakia, Syria

* Corresponding Author.

DOI https://doi.org/10.54216/IJNS.120203

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

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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

&nbsp 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. &nbsp

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 Reﬁned 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

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Abobala, Mohammad. "n-Cyclic Refined Neutrosophic Algebraic Systems of Sub-Indeterminacies, An Application to Rings and Modules." International Journal of Neutrosophic Science, vol. Volume 12, no. Issue 2, 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, Volume 12(Issue 2), 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 Volume 12, no. Issue 2 (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, Volume 12(Issue 2), pp. 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. 2020;Volume 12(Issue 2):81-95. DOI: https://doi.org/10.54216/IJNS.120203

M. Abobala, "n-Cyclic Refined Neutrosophic Algebraic Systems of Sub-Indeterminacies, An Application to Rings and Modules," International Journal of Neutrosophic Science, vol. Volume 12, no. Issue 2, pp. 81-95, 2020. DOI: https://doi.org/10.54216/IJNS.120203

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