2836-7863ISSN (Online)
Volume 3 , Issue 1 , PP: 1-06, 2024 | Cite this article as | XML | Html | PDF | Full Length Article
Noor Edin Rabeh 1 *
Doi: https://doi.org/10.54216/NIF.030101
The objective of this paper is to study some of the elementary algebraic properties of 3-cyclic refined neutrosophic matrices with real entries, where we study the algebraic structure of the multiplication operation and its properties such as associativity, commutativity, and the existence of algebraic multiplication inverse. Also, we illustrate many examples that explain the validity of our work.
3-cyclic refined neutrosophic matrix , Inverse , Associative , Indeterminacy
[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] Sankari, H. Abobala, M. (2023). On a Generalization of RSA Crypto-system by using 2-Cyclic Refined Integers. Journal of Cybersecurity and Information Management, 12(1), 67-73. DOI: https://doi.org/10.54216/JCIM.120106
[10] Abobala, M., Sankari, H., & Zeina, M. (2024). On novel security systems based on the 2-cyclic refined integers and the foundations of 2-cyclic refined number theory. Journal of Fuzzy Extension and Applications, 5(1), 69-85. doi: 10.22105/jfea.2024.423818.1321
[11] Abobala, M., “n-Cyclic Refined Neutrosophic Algebraic Systems of Sub-Indeterminacies, an Application to Rings and Modules", International Journal of Neutrosophic Science, 2020.
[12] Aswad, M., "n-Cyclic Refined Neutrosophic Vector Spaces and Matrices", Neutrosophic Knowledge, 2021.
[13] Ali, R., "n-Cyclic Refined Neutrosophic Groups", International Journal of Neutrosophic Science, 2021.
[14] 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.
