1
University of Debrecen, Department of Mathematical and Computational Science, Debrecen, Hungary
(badjajiann6math@gmail.com)
2
Universidad Regional Autónoma de los Andes Sede Babahoyo (UNIANDES Babahoyo). Ecuador
(direccionbabahoyo@uniandes.edu.ec)
3
Universidad Regional Autónoma de los Andes (UNIANDES Babahoyo), Ecuador
(ub.coordinacionac@uniandes.edu.ec)
Abstract :
This paper aims to solve the group of units problem for 3-cyclic real and rational refined neutrosophic rings and 4-cyclic real and rational refined neutrosophic rings, where ring isomorphisms between the real/rational 3-cyclic and 4-cyclic refined neutrosophic rings and the direct product of some field extensions of Q and R. These isomorphisms will help in classifying the group of units of each studied ring in terms of direct products of classical well-known abelian groups. Also, we use the classification isomorphisms to determine all ideals in these classes of algebraic rings.
Keywords :
3-cyclic refined neutrosophic ring; 4-cyclic refined neutrosophic ring; Von Shtawzen's group; group of units
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] 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.
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MLA | Narek Badjajian, 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, Vol. 23, No. 2, 2024 ,PP. 26-31 (Doi : https://doi.org/10.54216/IJNS.230203) |
APA | Narek Badjajian, Maikel Leyva Vazquez, Batista Hernández Noel. (2024). On The Classification of 3-Cyclic/4-Cyclic Refined Neutrosophic Real and Rational Von Shtawzen's Group. Journal of International Journal of Neutrosophic Science, 23 ( 2 ), 26-31 (Doi : https://doi.org/10.54216/IJNS.230203) |
Chicago | Narek Badjajian, Maikel Leyva Vazquez, Batista Hernández Noel. "On The Classification of 3-Cyclic/4-Cyclic Refined Neutrosophic Real and Rational Von Shtawzen's Group." Journal of International Journal of Neutrosophic Science, 23 no. 2 (2024): 26-31 (Doi : https://doi.org/10.54216/IJNS.230203) |
Harvard | Narek Badjajian, Maikel Leyva Vazquez, Batista Hernández Noel. (2024). On The Classification of 3-Cyclic/4-Cyclic Refined Neutrosophic Real and Rational Von Shtawzen's Group. Journal of International Journal of Neutrosophic Science, 23 ( 2 ), 26-31 (Doi : https://doi.org/10.54216/IJNS.230203) |
Vancouver | Narek Badjajian, Maikel Leyva Vazquez, Batista Hernández Noel. On The Classification of 3-Cyclic/4-Cyclic Refined Neutrosophic Real and Rational Von Shtawzen's Group. Journal of International Journal of Neutrosophic Science, (2024); 23 ( 2 ): 26-31 (Doi : https://doi.org/10.54216/IJNS.230203) |
IEEE | Narek Badjajian, Maikel Leyva Vazquez, Batista Hernández Noel, On The Classification of 3-Cyclic/4-Cyclic Refined Neutrosophic Real and Rational Von Shtawzen's Group, Journal of International Journal of Neutrosophic Science, Vol. 23 , No. 2 , (2024) : 26-31 (Doi : https://doi.org/10.54216/IJNS.230203) |