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International Journal of Neutrosophic Science
Volume 23 , Issue 2, PP: 26-31 , 2024 | Cite this article as | XML | Html |PDF

Title

On The Classification of 3-Cyclic/4-Cyclic Refined Neutrosophic Real and Rational Von Shtawzen's Group

  Narek Badjajian 1 * ,   Maikel Leyva Vazquez 2 ,   Batista Hernández Noel 3

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)

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Doi   :   https://doi.org/10.54216/IJNS.230203

Received: June 19, 2023 Revised: October 15, 2023 Accepted: November 18, 2023

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.

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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.

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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.

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[12] Abobala, M., " n-Cyclic Refined Neutrosophic Algebraic Systems of Sub-Indeterminacies, An Application to Rings and Modules", International Journal of Neutrosophic Science, 2020.

 

Cite this Article as :
Style #
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)
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