179 112
Full Length Article
Volume 12 , Issue2, PP: 81-95 , 2020

Title

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

Authors Names :   Mohammad Abobala   1  

1  Affiliation :  Faculty of Science, Tishreen University, Lattakia, Syria

    Email :  mohammadabobala777@gmail.com



Doi   :  10.5281/zenodo.4278999

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 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