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Title

The Structure of Imperfect Triplets in Several Refined Neutrosophic Rings

  Mikail Bal 1 * ,   Katy D. Ahmad 2 ,   Arwa A. Hajjari 3 ,   Rozina Ali 4

1  Gaziantep University, Turkey
    (mikailbal46@hotmail.com)

2  Islamic University Of Gaza, Palestine
    (katyon765@gmail.com)

3  Cairo University, Egypt
    (ArwaA.Hajjari22@gmail.com)

4  Cairo university, Egypt
    (rozyyy123n@gmail.com)

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Doi   :   https://doi.org/10.54216/JNFS.020103

Received July 25, 2021 Accepted: Jan 05, 2022

Abstract :

This paper solves the imperfect triplets problem in refined neutrosophic rings, where it presents the necessary and sufficient conditions for a triple  (x,y,z) to be an imperfect triplet in any refined neutrosophic ring. Also, this work introduces a full description of the structure of imperfect triplets in numerical refined neutrosophic rings such as refined neutrosophic ring of integers Z(I1,I2) , refined neutrosophic ring of rationales Q(I1,I2), and refined neutrosophic ring or real numbers  (R(I1,I2). 

Keywords :

Refined Neutrosophic Ring, imperfect Duplet, Imperfect triplet

References :

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

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

 [3] Kandasamy, V., Kandasamy, I., and Smarandache, F., " Algebraic Structure of Neutrosophic Duplets In Neutrosophic Rings <Z∪I>,<Q∪I>,and<R∪I> ", Neutrosophic Sets and Systems, Vol.23, pp.85-95, 2018.

[4] Kandasamy, V. W. B,. Ilanthenral, K., and Smarandache, F., " Semi-Idempotents in Neutrosophic Rings", Mathematics Journal (MDPI), Vol. 7, 2019.

[5] 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. 

[6] 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. 

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

[8] Kandasamy, V., Kandasamy, I., and Smarandache, F., "Neutrosophic Duplets of {Z_(p^n ),×} and {Z_pq,×} and Their Properties", Symmetry, 2018. 

[9] Yingcang, Ma., Xiaohong Zhang ., Smarandache, F., and  Juanjuan, Z., The Structure of Idempotents in Neutrosophic Rings and Neutrosophic Quadruple Rings, Symmetry, Vol. 11, 2019.

[10] Kandasamy, V., Kandasamy, I., and Smarandache, F., "Neutrosophic Triplets In Neutrosophic Rings", Mathematics, 2019.

 [11] 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.

[12] Florentin Smarandache, Neutrosophic Duplet Structures, Joint Fall 2017 Meeting of the Texas Section of the APS, Texas Section of the AAPT, and Zone 13 of the Society of Physics Students,  The University of Texas at Dallas, Richardson, TX, USA, October 20-21, 2017,  http://meetings.aps.org/Meeting/TSF17/Session/F1.32

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

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

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

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

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

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

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

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

[21] Abobala, M., Bal, M., and Hatip, A.," A Review On Recent Advantages In Algebraic Theory Of Neutrosophic Matrices", International Journal of Neutrosophic Science, Vol. 17, 2021.

[22] Hajjari, A., and Ali, R., " A Contribution To Kothe's Conjecture In Refined Neutrosophic Rings", International Journal of Neutrosophic Science", Vol. 16, 2021.

 [23] Olgun, N., Hatip, A., Bal, M., and Abobala, M., " A Novel Approach To Necessary and Sufficient Conditions For The Diagonalization of Refined Neutrosophic Matrices", International Journal of Neutrosophic Science, Vol. 16, pp. 72-79, 2021.

[24] Abobala, M., Hatip, A., Bal,M.," A Study Of Some Neutrosophic Clean Rings", International journal of neutrosophic science, 2022.

[25] Abobala, M., Bal, M., Aswad, M., "A Short Note On Some Novel Applications of Semi Module Homomorphisms", International journal of neutrosophic science, 2022.

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

[27] Chalapathi, T., and Kumar, K.,"Neutrosophic Units of Neutrosophic Rings and Fields", Neutrosophic Sets and Systems, Vol. 21, 2018.

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

[29] Smarandache, F., and Broumi,M., "Neutro-Intelligent Set is a particular case of the refined neutrosophic set", Journal of Neutrosophic and Fuzzy Systems, Vol. 1, 2022.

[30] Ahmad, K., Bal, M., and Aswad, M.," The kernel of Fuzzy and Anti Fuzzy Groups",Journal of Neutrosophic and Fuzzy Systems, Vol.1, 2022.

 [31] Ahmad, K., Bal, M., and Aswad, M.," A Short Note on The Solution Of Fermat's Diophantine Equation In Some Neutrosophic Rings", Journal of Neutrosophic and Fuzzy Systems, Vol. 1, 2022.

[32] Singh, P, K., Ahmad, K., Bal, M., Aswad, M.," On The Symbolic Turiyam Rings", Journal of Neutrosophic and Fuzzy Systems, 2022.

[33] Sankari, H, and Abobala, M, " A Contribution to m-Power Closed Groups", UMM-Alqura University Journal for Applied Sciences, KSA, 2020.

[34] Singh, P,K., " Data With Turiyam Set for Fourth Dimension Quantum Information Processing", Journal of Neutrosophic and Fuzzy Systems, vol.1, 2022.

 [35] Singh, P,K., " Anti-geometry and NeutroGeometry Characterization of Non-Euclidean Data", Journal of Neutrosophic and Fuzzy Systems, vol. 1, 2022

[36] Abobala, M., "On Some Neutrosophic Algebraic Equations", Journal of New Theory, Vol. 33, 2020.

[37] 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.

[38] Ahmad, K., Bal, M., Hajjari, A., Ali, R.," On Imperfect Duplets In Some refined Neutrosophic Rings", Journal of Neutrosophic and Fuzzy Systems, 2022.

[37] Prem Kumar Singh, NeutroAlgebra and NeutroGeometry for Dealing Heteroclinic Patterns. In: Theory and Applications of NeutroAlgebras as Generalizations of Classical Algebras, IGI Global Publishers, April 2022, Chapter 6,  DOI: 10.4018/978-1-6684-3495-6, ISBN13: 9781668434956

[38] Prem Kumar Singh, AntiGeometry and NeutroGeometry Characterization of Non-Euclidean Data Sets, Journal of Neutrosophic and Fuzzy Systems, Nov 2021, Volume 1, Issue 1, pp. 24-33, ISSN: ,  DOI: https://doi.org/10.54216/JNFS.0101012   

[39] Prem Kumar Singh, Three-way n-valued neutrosophic concept lattice at different granulation, International Journal of Machine Learning and Cybernetics, Springer, November 2018, Vol 9, Issue 11, pp. 1839-1855,

Cite this Article as :
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MLA Mikail Bal, Katy D. Ahmad, Arwa A. Hajjari, Rozina Ali. "The Structure of Imperfect Triplets in Several Refined Neutrosophic Rings." Full Length Article, Vol. 2, No. 1, 2022 ,PP. 21-30 (Doi   :  https://doi.org/10.54216/JNFS.020103)
APA Mikail Bal, Katy D. Ahmad, Arwa A. Hajjari, Rozina Ali. (2022). The Structure of Imperfect Triplets in Several Refined Neutrosophic Rings. Journal of Full Length Article, 2 ( 1 ), 21-30 (Doi   :  https://doi.org/10.54216/JNFS.020103)
Chicago Mikail Bal, Katy D. Ahmad, Arwa A. Hajjari, Rozina Ali. "The Structure of Imperfect Triplets in Several Refined Neutrosophic Rings." Journal of Full Length Article, 2 no. 1 (2022): 21-30 (Doi   :  https://doi.org/10.54216/JNFS.020103)
Harvard Mikail Bal, Katy D. Ahmad, Arwa A. Hajjari, Rozina Ali. (2022). The Structure of Imperfect Triplets in Several Refined Neutrosophic Rings. Journal of Full Length Article, 2 ( 1 ), 21-30 (Doi   :  https://doi.org/10.54216/JNFS.020103)
Vancouver Mikail Bal, Katy D. Ahmad, Arwa A. Hajjari, Rozina Ali. The Structure of Imperfect Triplets in Several Refined Neutrosophic Rings. Journal of Full Length Article, (2022); 2 ( 1 ): 21-30 (Doi   :  https://doi.org/10.54216/JNFS.020103)
IEEE Mikail Bal, Katy D. Ahmad, Arwa A. Hajjari, Rozina Ali, The Structure of Imperfect Triplets in Several Refined Neutrosophic Rings, Journal of Full Length Article, Vol. 2 , No. 1 , (2022) : 21-30 (Doi   :  https://doi.org/10.54216/JNFS.020103)
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