883 888
Full Length Article
International Journal of Neutrosophic Science
Volume 16 , Issue 2, PP: 80-87 , 2021 | Cite this article as | XML | Html |PDF

Title

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)

Full Text Download


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 Systems, vol. 5, pp. 9-14, 2014.

 [22] Anuradha V. S., "Neutrosophic Fuzzy Hierarchical Clustering for Dengue Analysis in Sri Lanka", Neutrosophic Sets and Systems, vol. 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 :
Style #
MLA Arwa A. Hajjari, Rozina Ali. "A Contribution To Kothe's Conjecture In Refined Neutrosophic Rings." International Journal of Neutrosophic Science, Vol. 16, No. 2, 2021 ,PP. 80-87 (Doi   :  https://doi.org/10.54216/IJNS.160203)
APA Arwa A. Hajjari, Rozina Ali. (2021). A Contribution To Kothe's Conjecture In Refined Neutrosophic Rings. Journal of International Journal of Neutrosophic Science, 16 ( 2 ), 80-87 (Doi   :  https://doi.org/10.54216/IJNS.160203)
Chicago Arwa A. Hajjari, Rozina Ali. "A Contribution To Kothe's Conjecture In Refined Neutrosophic Rings." Journal of International Journal of Neutrosophic Science, 16 no. 2 (2021): 80-87 (Doi   :  https://doi.org/10.54216/IJNS.160203)
Harvard Arwa A. Hajjari, Rozina Ali. (2021). A Contribution To Kothe's Conjecture In Refined Neutrosophic Rings. Journal of International Journal of Neutrosophic Science, 16 ( 2 ), 80-87 (Doi   :  https://doi.org/10.54216/IJNS.160203)
Vancouver Arwa A. Hajjari, Rozina Ali. A Contribution To Kothe's Conjecture In Refined Neutrosophic Rings. Journal of International Journal of Neutrosophic Science, (2021); 16 ( 2 ): 80-87 (Doi   :  https://doi.org/10.54216/IJNS.160203)
IEEE Arwa A. Hajjari, Rozina Ali, A Contribution To Kothe's Conjecture In Refined Neutrosophic Rings, Journal of International Journal of Neutrosophic Science, Vol. 16 , No. 2 , (2021) : 80-87 (Doi   :  https://doi.org/10.54216/IJNS.160203)
↑