International Journal of Neutrosophic Science

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https://doi.org/10.54216/IJNS

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Volume 16 , Issue 2 , PP: 80-87, 2021 | Cite this article as | XML | Html | PDF | Full Length Article

A Contribution To Kothe's Conjecture In Refined Neutrosophic Rings

Arwa A. Hajjari 1 * , Rozina Ali 2

  • 1 Cairo University, Egypt - (ArwaA.Hajjari22@gmail.com)
  • 2 Cairo University, Egypt - (rozyyy123n@gmail.com)
  • Doi: https://doi.org/10.54216/IJNS.160203

    Received: August 02, 2021 Accepted: November 06, 2021
    Abstract

    The objective of this paper is to answer an open question asked in [42], about the equivalence between Kothe's conjecture in a ring R and its corresponding refined neutrosophic ring . Where it proves that Kothe's conjecture is true in R if and only if it is true in .

    Keywords :

    refined neutrosophic ring,  , Kothe Conjecture,  , Nilpotent Ideal.

    References

    [1] Smarandache, F., " A Unifying Field in Logics: Neutrosophic Logic, Neutrosophy, Neutrosophic Set, Neutrosophic Probability", American Research Press. Rehoboth, 2003.

    [2]  Edalatpanah. S.A., "Systems of Neutrosophic Linear Equations", Neutrosophic Sets and Systems, Vol. 33, pp. 92-104. 2020.

    [3] Sankari, H., and Abobala, M., "Neutrosophic Linear Diophantine Equations With two Variables", Neutrosophic Sets and Systems, Vol. 38, pp. 22-30, 2020.

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

    [5] Abobala, M., "On The Characterization of Maximal and Minimal Ideals In Several Neutrosophic Rings", Neutrosophic Sets and Systems, Vol. 45, 2021.

     [6] Kandasamy, V.W.B., and Smarandache, F., "Some Neutrosophic Algebraic Structures and Neutrosophic N-Algebraic Structures", Hexis, Phonex, Arizona, 2006.

    [7] Agboola, A.A.A., Akinola, A.D., and Oyebola, O.Y., " Neutrosophic Rings I" , International J.Mathcombin, Vol 4,pp 1-14. 2011

    [8] Agboola, A.A.A., "On Refined Neutrosophic Algebraic Structures," Neutrosophic Sets and Systems,Vol.10, pp. 99-101. 2015.

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

    [10] Ibrahim, M., and Abobala, M., "An Introduction To Refined Neutrosophic Number Theory", Neutrosophic Sets and Systems, Vol. 45, 2021.

    [11] Kandasamy, I., Kandasamy, V., and Smarandache, F., "Algebraic structure of Neutrosophic Duplets in Neutrosophic Rings", Neutrosophic Sets and Systems, Vol. 18, pp. 85-95. 2018.

    [12] Yingcang, Ma., Xiaohong Zhang ., Smarandache, F., and  Juanjuan, Z., "The Structure of Idempotents in Neutrosophic Rings and Neutrosophic Quadruple Rings", Symmetry Journal (MDPI), Vol. 11. 2019.

     [13] Kandasamy, V. W. B,. Ilanthenral, K., and Smarandache, F., "Semi-Idempotents in Neutrosophic 

    [14] Smarandache, F., and Ali, M., "Neutrosophic Triplet Group", Neural. Compute. Appl. 2019.

    [15] Sankari, H., and Abobala, M.," AH-Homomorphisms In neutrosophic Rings and Refined Neutrosophic Rings", Neutrosophic Sets and Systems, Vol. 38, pp. 101-112, 2020.

    [16] Smarandache, F., and Kandasamy, V.W.B., " Finite Neutrosophic Complex Numbers",·Source: arXiv. 2011.

    [17] Ali, Rozina., " On the Concept of Algebraic Actions In Neutrosophic Groups", Resaechgate.net, 2021.

    [18] Ali, Rozina., " Neutrosophic Matrices and Their Properties", researchgat.net, 2021.

    [19] Ali, Rozina., " Recent Advantages In Neutrosophic Module Theory", researchgate.net, 2021.

    [20] Smarandache, F., "Neutrosophic Set a Generalization of the Intuitionistic Fuzzy Sets", Inter. J. Pure Appl. Math.pp. 287-297. 2005.

    [21] M. Ali, F. Smarandache, M. Shabir and L. Vladareanu.,  "Generalization of Neutrosophic Rings and Neutrosophic Fields", Neutrosophic Sets and Systemsvol. 5, pp. 9-14, 2014.

     [22] Anuradha V. S., "Neutrosophic Fuzzy Hierarchical Clustering for Dengue Analysis in Sri Lanka", Neutrosophic Sets and Systemsvol. 31, pp. 179-199. 2020.

    [23] Olgun, N., and  Hatip, A.,  "The Effect Of The Neutrosophic Logic On The Decision Making, in Quadruple Neutrosophic Theory And Applications", Belgium, EU, Pons Editions Brussels,pp. 238-253. 2020.

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

    [25] Abobala, M., "Maximality and Minimality of ideals In Some Neutrosophic Rings", Hal-Archives, 2021.

    [26] 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.

    [27] Smarandache, F., " n-Valued Refined Neutrosophic Logic and Its Applications in Physics", Progress in Physics, 143-146, Vol. 4, 2013.

    [28] Adeleke, E.O., Agboola, A.A.A.,and Smarandache, F.,  "Refined Neutrosophic Rings I", International Journal of Neutrosophic Science, Vol. 2(2), pp. 77-81. 2020.

     [29] Sankari, H., and Abobala, M., "Solving Three Conjectures About Neutrosophic Quadruple Vector Spaces", Neutrosophic Sets and Systems, Vol. 38, pp. 70-77. 2020.

    [30] 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.

    [31] Abobala, M., On Refined Neutrosophic Matrices and Their Applications In Refined Neutrosophic Algebraic Equations, Journal Of Mathematics, Hindawi, 2021

    [32] Abobala, M., A Study of Maximal and Minimal Ideals of n-Refined Neutrosophic Rings, Journal of Fuzzy Extension and Applications, Vol. 2, pp. 16-22, 2021.

    [33] Abobala, M., " Semi Homomorphisms and Algebraic Relations Between Strong Refined Neutrosophic Modules and Strong Neutrosophic Modules", Neutrosophic Sets and Systems, Vol. 39, 2021.

    [34] Abobala, M., On The Representation of Neutrosophic Matrices by Neutrosophic Linear Transformations, Journal of Mathematics, Hindawi, 2021. 

    [35] Abobala, M., "On Some Algebraic Properties of n-Refined Neutrosophic Elements and n-Refined Neutrosophic Linear Equations", Mathematical Problems in Engineering, Hindawi, 2021

    [36] Kandasamy V, Smarandache F., and Kandasamy I., Special Fuzzy Matrices for Social Scientists . Printed in the United States of America,2007, book, 99 pages.

     [37] Khaled, H., and Younus, A., and Mohammad, A., " The Rectangle Neutrosophic Fuzzy Matrices", Faculty of Education Journal Vol. 15, 2019. (Arabic version).

    [38] Abobala, M., Partial Foundation of Neutrosophic Number Theory, Neutrosophic Sets and Systems, Vol. 39 , 2021.

    [39] F. Smarandache, Neutrosophic Theory and Applications, Le Quy Don Technical University, Faculty of Information technology, Hanoi, Vietnam, 17th May 2016.

     [40] Sankari, H, and Abobala, M., " On A New Criterion For The Solvability of non Simple Finite Groups and m-Abelian Solvability", Journal of Mathematics, Hindawi, 2021.

    [41] Giorgio, N, Mehmood, A., and Broumi, S.," Single Valued neutrosophic Filter", International Journal of Neutrosophic Science, Vol. 6, 2020.

    [42] Abobala, M., "A Study Of Nil Ideals and Kothe's Conjecture In Neutrosophic Rings", International Journal of Mathematics and Mathematical Sciences, hindawi, 2021

    [43] 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.

     [44] Abobala, M., "Neutrosophic Real Inner Product Spaces", Neutrosophic Sets and Systems, Vol. 43, 2021.

    [45] Abobala, M., "On Some Special Elements In Neutrosophic Rings and Refined Neutrosophic Rings", Journal of New Theory, vol. 33, 2020.

    [46] Abobala, M., and Hatip, A., "An Algebraic Approch To Neutrosophic Euclidean Geometry", Neutrosophic Sets and Systems, Vol. 43, 2021.

     

    Cite This Article As :
    A., Arwa. , Ali, Rozina. A Contribution To Kothe's Conjecture In Refined Neutrosophic Rings. International Journal of Neutrosophic Science, vol. , no. , 2021, pp. 80-87. DOI: https://doi.org/10.54216/IJNS.160203
    A., A. Ali, R. (2021). A Contribution To Kothe's Conjecture In Refined Neutrosophic Rings. International Journal of Neutrosophic Science, (), 80-87. DOI: https://doi.org/10.54216/IJNS.160203
    A., Arwa. Ali, Rozina. A Contribution To Kothe's Conjecture In Refined Neutrosophic Rings. International Journal of Neutrosophic Science , no. (2021): 80-87. DOI: https://doi.org/10.54216/IJNS.160203
    A., A. , Ali, R. (2021) . A Contribution To Kothe's Conjecture In Refined Neutrosophic Rings. International Journal of Neutrosophic Science , () , 80-87 . DOI: https://doi.org/10.54216/IJNS.160203
    A. A. , Ali R. [2021]. A Contribution To Kothe's Conjecture In Refined Neutrosophic Rings. International Journal of Neutrosophic Science. (): 80-87. DOI: https://doi.org/10.54216/IJNS.160203
    A., A. Ali, R. "A Contribution To Kothe's Conjecture In Refined Neutrosophic Rings," International Journal of Neutrosophic Science, vol. , no. , pp. 80-87, 2021. DOI: https://doi.org/10.54216/IJNS.160203