International Journal of Neutrosophic Science

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https://doi.org/10.54216/IJNS

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Volume 23 , Issue 2 , PP: 26-31, 2024 | Cite this article as | XML | Html | PDF | Full Length Article

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)
  • 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.

    [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.

     

    Cite This Article As :
    Badjajian, Narek. , Leyva, Maikel. , Hernández, Batista. 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, pp. 26-31. DOI: https://doi.org/10.54216/IJNS.230203
    Badjajian, N. Leyva, M. Hernández, B. (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
    Badjajian, Narek. Leyva, Maikel. Hernández, Batista. 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
    Badjajian, N. , Leyva, M. , Hernández, B. (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
    Badjajian N. , Leyva M. , Hernández B. [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
    Badjajian, N. Leyva, M. Hernández, B. "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, pp. 26-31, 2024. DOI: https://doi.org/10.54216/IJNS.230203