Volume 9 • Issue 1 • PP: 19-27 • 2024
On the Classification of 3-Cyclic Refined Real Vector Spaces and Related Inner Products
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© 2024 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
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This paper is concerned with the study of the classification of 3-cyclic refined real vector spaces by semi-module isomorphisms, where we use this algebraic technique to find the algebraic relationship between real 3-cyclic refined vector spaces and classical vector spaces. Also, we define the inner products on these spaces and prove many related inequalities.
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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 andOpen 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] D. G. Northcott, Lessons on Rings, Modules, and Multiplicities, Cambridge Univ. Press, Cambridge, 1968.
[10] A. G. A¯garg¨um, D. D. Anderson and S. Valdes-Leon, Factorization in commutative rings with zero divisors, III, Rocky Mountain J. Math. 31 (2001), 1–21.
[11] D. D. Anderson and R. Markanda, Unique factorization rings with zero divisors, Houston J. Math. 11 (1985), 15–30.
[12] Abobala, M., “n-Cyclic Refined Neutrosophic Algebraic Systems of Sub-Indeterminacies, an Application to Rings and Modules", International Journal of Neutrosophic Science, 2020.
[13] Aswad, M., "n-Cyclic Refined Neutrosophic Vector Spaces and Matrices", Neutrosophic Knowledge, 2021.
[14] Ali, R., "n-Cyclic Refined Neutrosophic Groups", International Journal of Neutrosophic Science, 2021.
[15] Rama Asad Nadweh, Rozina Ali, Maretta Sarkis, "On the Algebraic Properties of 2-Cyclic Refined Neutrosophic Matrices and the Diagonalization Problem", Neutrosophic Sets and Systems, Vol 54, 2023.
[16] Sadiq. B., “A Contribution To The group Of Units Problem in Some 2-Cyclic Refined Neutrosophic Rings ", International Journal of Neutrosophic Science, 2022.
[17] 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.
[18] Katy D. Ahmad, Mikail Bal, Arwa A. Hajjari, Rozina Ali. (2021). Novel Applications of Neutrosophic AH-Isometries to the Group of Units Problem in Neutrosophic Rings and Refined Neutrosophic Rings. Journal of Neutrosophic and Fuzzy Systems, 1 (2), 89-98 (Doi : https://doi.org/10.54216/JNFS.010205).
[19] 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).
[20] Sankari, H. Abobala, M. (2024). On The Computational Properties of 3-Cyclic and 4-Cyclic Refined Matrices and the Diagonalization Algorithm. International Journal of Advances in Applied Computational Intelligence, 37-45. DOI: https://doi.org/10.54216/IJAACI.060204
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