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Title

An Introduction to The Symbolic Turiyam Groups and AH-Substructures

  A. Alrida Basheer 1 * ,   Katy D. Ahmad 2 ,   Rozina Ali 3

1  Imam Kadhum College, Iraq
    (basheerabdalrida66n@gmail.com)

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

3  Cairo University, Egypt
    (rozyyy123n@gmail.com)


Doi   :   https://doi.org/10.54216/JNFS.030205

Received: April 05, 2022 Accepted: July 16, 2022

Abstract :

The aim of This paper is to define for the first time the concept of symbolic Turiyam group. This work is devoted to     study some elementary properties of symbolic Turiyam groups and to establish the algebraic basis of this structure such as symbolic Turiyam subgroups, symbolic Turiyam homomorphisms, and symbolic Turiyam isomorphisms.

Keywords :

symbolic Turiyam group , symbolic Turiyam subgroup , symbolic Turiyam homomorphism.

References :

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

[2] Alhamido, R., and Gharibah, T., "Neutrosophic Crisp Tri-Topological Spaces", Journal of New Theory, Vol. 23 , pp.13-21. 2018.

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

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

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

[6] Alhamido, R., and Abobala, M., "AH-Substructures in Neutrosophic Modules", International Journal of Neutrosophic Science, Vol. 7, pp. 79-86 . 2020.

[7] Abobala, M., "AH-Subspaces in Neutrosophic Vector Spaces", International Journal of Neutrosophic Science, Vol. 6 , pp. 80-86. 2020.

[8] Abobala, M.,. "A Study of AH-Substructures in n-Refined Neutrosophic Vector Spaces", International Journal of Neutrosophic Science", Vol. 9, pp.74-85. 2020.

[9] Hatip, A., Alhamido, R., and Abobala, M., "A Contribution to Neutrosophic Groups", International Journal of Neutrosophic Science", Vol. 0, pp. 67-76 . 2019.

[10] Abobala, M., " n-Refined Neutrosophic Groups I", International Journal of Neutrosophic Science, Vol. 0, pp. 27-34. 2020.

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

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

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

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

[15] Smarandache, F., and Abobala, M., n-Refined neutrosophic Rings, International Journal of Neutrosophic Science, Vol. 5 , pp. 83-90, 2020.

[16] 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.

[17] 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.

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

 [19] Abobala, M., On Some Special Substructures of Neutrosophic Rings and Their Properties, International Journal of Neutrosophic Science", Vol. 4 , pp. 72-81, 2020.

[20] Smarandache, F., " An Introduction To neutrosophic Genetics", International Journal of neutrosophic Science, Vol.13, 2021.

[21] Martin, N, Smarandache, F, and Broumi, S., " Covid 19 Decision Making using Extended Plithogenic hypersoft Sets With Dual Dominent Attributes", International Journal of neutrosophic Science, Vol. 13, 2021.

[22]Agboola, A.A., "Introduction To Neutro groups", International Journal of neutrosophic Science, Vol. 6, 2020.

[23] Abobala, M., "On Some Special Substructures of Refined Neutrosophic Rings", International Journal of Neutrosophic Science, Vol. 5, pp. 59-66. 2020.

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

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

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

[27]. Abobala, M., " n-Refined Neutrosophic Groups II", International Journal of Neutrosophic Science, Vol. 0, 2020.

[28] 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.

[29] Aswad, F, M., " A Study of Neutrosophic Complex Number and Applications", Neutrosophic Knowledge, Vol. 1, 2020.

[30] Aswad, M., " A Study of The Integration Of Neutrosophic Thick Function", International journal of neutrosophic Science, 2020.

[31] Abobala, M, "n-Cyclic Refined Neutrosophic Algebraic Systems Of Sub-Indeterminacies, An Application To Rings and Modules", International Journal of Neutrosophic Science, Vol. 12, pp. 81-95 . 2020.

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

[33] 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.

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

[35] 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.

[36] 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.

[37] Turksen, I., "Interval valued fuzzy sets based on normal forms", Fuzzy Sets and Systems, 20, pp.191-210, 1986. 1986.

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

[39] Abobala, M., "Classical Homomorphisms Between n-refined Neutrosophic Rings", International Journal of Neutrosophic Science", Vol. 7, pp. 74-78. 2020.

[40] 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.

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

[42] 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.

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

 [44] Hatip, A., and Olgun, N.,  "On Refined Neutrosophic R-Module", International Journal of Neutrosophic Science, Vol. 7, pp.87-96. 2020.

[45] Bal, M., and Abobala, M., "On The Representation Of Winning Strategies Of Finite Games By Groups and Neutrosophic Groups", Journal Of Neutrosophic and Fuzzy Systems, 2022.

[46] Smarandache F., and Abobala, M.,  "n-Refined Neutrosophic Vector Spaces", International Journal of Neutrosophic Science, Vol. 7, pp. 47-54. 2020.

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

[48] 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.

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

[50] 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.

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

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

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

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

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

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

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

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

 [59] 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.

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

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

[62] 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.

[63]Alhamido, K., R., "A New Approach of neutrosophic Topological Spaces", International Journal of neutrosophic Science, Vol.7, 2020.

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

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

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

[67] Sundar, J., Vadivel, A., " New operators Using Neutrosophic Open Sets", Journal Of Neutrosophic and Fuzzy Systems, 2022.

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

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

 [70] Chellamani, P., and Ajay, D., "Pythagorean neutrosophic Fuzzy Graphs", International Journal of Neutrosophic Science, Vol. 11, 2021.

[71] Singh P. K., “Fourth dimension data representation and its analysis using Turiyam Context”, Journal of Computer and Communications, 2021, Vol. 9, no. 6, pp. 222-229,DOI: 10.4236/jcc.2021.96014, https://www.scirp.org/journal/paperinformation.aspx?paperid=110694

[72] Singh P. K., “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

 [73] Singh P. K., “Three-way n-valued neutrosophic concept lattice at different granulation”, International Journal of Machine Learning and Cybernetics, Vol 9, Issue 11, pp. 1839-1855, 2018.

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

[75] Singh P. K., “AntiGeometry and NeutroGeometry Characterization of Non-Euclidean Data Sets”, Journal of Neutrosophic and Fuzzy Systems, Vol 1, Issue 1, pp. 24-33, 2021,  ,  DOI: https://doi.org/10.54216/JNFS.0101012

[76] Singh, P,K., " Anti-geometry and NeutroGeometry Characterization of Non-Euclidean Data", Journal of Neutrosophic and Fuzzy Systems, Volume 1, Issue 1, pp. 24-33, 2021.

[77] Singh, P,K., " Data With Turiyam Set for Fourth Dimension Quantum Information Processing", Journal of Neutrosophic and Fuzzy Systems, Volume 1, Issue 1, pp. 9-23, 2021.

[78] Singh, P, K., Ahmad, K., Bal, M., Aswad, M.," On The Symbolic Turiyam Rings", Journal of Neutrosophic and Fuzzy Systems, Vol. 1 , No. 2 , pp. 80-88 , 2021

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

[80] Bal, M.,, Singh, P. K., Ahmad, K., and Aswad, M., " A Short Introduction To The Concept Of Symbolic Turiyam Matrix", Neutrosophic and Fuzzy Systems, Vol. 2 , No. 1 , pp. 88-99 , 2022. 

[81] Bal, M., Singh, P. K, and Ahmad, K., " An Introduction To The Symbolic Turiyam R-Modules and Turiyam Modulo Integers", Neutrosophic and Fuzzy Systems, Vol. 2, No. 2 , pp. 8-19,2022.

[82] Bal, M., Singh, P. K, and Ahmad, K., " An Introduction To The Symbolic Turiyam Vector Spaces and Complex Numbers", Neutrosophic and Fuzzy Systems, Vol. 2 , No. 1 , pp. 76-87 , Mar 2022.

[83] Singh P. K., “Non-Euclidean, Anti-Geometry and NeutroGeometry Characterization”, International Journal of Neutrosophic Sciences, Vol 18, Issue 3, pp. 8-19, 2022.

[84] Singh P. K., “Data with Non-Euclidean Geometry and its Characterization”. Journal of Artificial Intelligence and Technology, Vol 2, Issue 1, pp. 3-8, 2022, DOI: 10.37965/jait.2021.12001 


Cite this Article as :
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MLA A. Alrida Basheer , Katy D. Ahmad, Rozina Ali. "An Introduction to The Symbolic Turiyam Groups and AH-Substructures." Full Length Article, Vol. 3, No. 2, 2022 ,PP. 43-52 (Doi   :  https://doi.org/10.54216/JNFS.030205)
APA A. Alrida Basheer , Katy D. Ahmad, Rozina Ali. (2022). An Introduction to The Symbolic Turiyam Groups and AH-Substructures. Journal of Full Length Article, 3 ( 2 ), 43-52 (Doi   :  https://doi.org/10.54216/JNFS.030205)
Chicago A. Alrida Basheer , Katy D. Ahmad, Rozina Ali. "An Introduction to The Symbolic Turiyam Groups and AH-Substructures." Journal of Full Length Article, 3 no. 2 (2022): 43-52 (Doi   :  https://doi.org/10.54216/JNFS.030205)
Harvard A. Alrida Basheer , Katy D. Ahmad, Rozina Ali. (2022). An Introduction to The Symbolic Turiyam Groups and AH-Substructures. Journal of Full Length Article, 3 ( 2 ), 43-52 (Doi   :  https://doi.org/10.54216/JNFS.030205)
Vancouver A. Alrida Basheer , Katy D. Ahmad, Rozina Ali. An Introduction to The Symbolic Turiyam Groups and AH-Substructures. Journal of Full Length Article, (2022); 3 ( 2 ): 43-52 (Doi   :  https://doi.org/10.54216/JNFS.030205)
IEEE A. Alrida Basheer, Katy D. Ahmad, Rozina Ali, An Introduction to The Symbolic Turiyam Groups and AH-Substructures, Journal of Full Length Article, Vol. 3 , No. 2 , (2022) : 43-52 (Doi   :  https://doi.org/10.54216/JNFS.030205)