Volume 11 • Issue 2 • PP: 44-49 • 2024
The Mathematical Formulas of 2-Cyclic Refined Duplets and Triplets
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This work is dedicated to studying the problem of computing 2-cyclic refined neutrosophic duplets and triplets in the 2-cyclic refined neutrosophic ring of real numbers, where we present four different formulas that describe all possible duplets in this extended ring. Also, we present four different formulas for the computation of related triplets in the same ring.
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References
[1] Basheer, A., Ahmad, K., and Ali, R., “A Short Contribution to Von Shtawzen's Abelian Group in n-Cyclic Refined Neutrosophic Rings", Journal of Neutrosophic and Fuzzy Systems, 2022.
[2] Von Shtawzen, O., “Conjectures for Invertible Diophantine Equations of 3-Cyclic and 4-Cyclic Refined Integers", Journal of Neutrosophic and Fuzzy Systems, Vol.3, 2022.
[3] Von Shtawzen, O., “On a Novel Group Derived from a Generalization of Integer Exponents and Open Problems", Galoitica journal Of Mathematical Structures and Applications, Vol 1, 2022.
[4] Basheer, A., Ahmad, K., and Ali, R., “On Some Open Problems about n-Cyclic Refined Neutrosophic Rings and Number Theory", Journal of Neutrosophic and Fuzzy Systems, 2022.
[5] A. Alrida Basheer , Katy D. Ahmad , Rozina Ali., "Examples on Some Novel Diophantine Equations Derived from the Group of Units Problem in n-Cyclic Refined Neutrosophic Rings of Integers", Galoitica Journal Of Mathematical Structures And Applications, Vol.3, 2022.
[6] Sankari, H., and Abobala, M., “On the Group of Units Classification In 3-Cyclic and 4-cyclic Refined Rings of Integers and the Proof of Von Shtawzens' Conjectures", International Journal of Neutrosophic Science, 2023.
[7] Sankari, H., and Abobala, M., “On the Classification of the Group of Units of Rational and Real 2-Cyclic Refined Neutrosophic Rings", Neutrosophic Sets and Systems, 2023.
[8] Sankari, H., and Abobala, M., “On the Algebraic Homomorphisms between Symbolic 2-Plithogenic Rings And 2-cyclic Refined Rings", Neutrosophic Sets and Systems, 2023.
[9] Abobala, M., “n-Cyclic Refined Neutrosophic Algebraic Systems of Sub-Indeterminacies, an Application to Rings and Modules", International Journal of Neutrosophic Science, 2020.
[10] Aswad, M., "n-Cyclic Refined Neutrosophic Vector Spaces and Matrices", Neutrosophic Knowledge, 2021.
[11] Ali, R., "n-Cyclic Refined Neutrosophic Groups", International Journal of Neutrosophic Science, 2021.
[12] Sadiq. B., “A Contribution To The group Of Units Problem in Some 2-Cyclic Refined Neutrosophic Rings ", International Journal of Neutrosophic Science, 2022.
[13] Nabil Khuder Salman, Maikel Leyva Vazquez,Batista Hernández Noel. On The Classification of 3-Cyclic/4-Cyclic Refined Neutrosophic Real and Rational Von Shtawzen's Group. International Journal of Neutrosophic Science, (2024); 23 (2): 26-31.
[14] Ahmad Salama, Rasha Dalla, Malath Al Aswad, Rozina Ali. (2022). Some Results About 2-Cyclic Refined Neutrosophic Complex Numbers. Journal of Neutrosophic and Fuzzy Systems, 4 (1), 41-8 (Doi : https://doi.org/10.54216/JNFS.040105).
[15] Barry, W. Badjajian, N. (2024). Computing Idempotent Elements In 3-Cyclic and 4-Cyclic Refined Neutrosophic Rings of Integers. Journal of Neutrosophic and Fuzzy Systems, (), 31-38. DOI: https://doi.org/10.54216/JNFS.080104
[16] F. Smarandache, Neutrosophic Perspectives: Triplets, Duplets, Multisets, Hybrid Operators, Modal Logic, Hedge Algebras. And Applications. Pons Editions, Bruxelles, 323 p., 2017; CHAPTER IX: 127-134
[17] Florentin Smarandache and Mumtaz Ali, Neutrosophic Triplet Group, NeuralComputing and Applications, Springer, 1-7, 2016, https://link.springer.com/article/10.1007/s00521-016-2535-x; DOI: 10.1007/s00521-016-2535-x.
[18] Merkepci, H. D., K. (2022). On the Conditions of Imperfect Neutrosophic Duplets and Imperfect Neutrosophic Triplets. Galoitica: Journal of Mathematical Structures and Applications, (), 08-13. DOI: https://doi.org/10.54216/GJMSA.020201
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