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Volume 4 , Issue 1 , PP: 06-14, 2024 | Cite this article as | XML | Html | PDF | Full Length Article

On the Computation of Units in Symbolic 4- Plithogenic Ring of Integers

Lee Xu 1 *

  • 1 University of Chinese Academy of Sciences, CAS, Mathematics Department, Beijing, China - (Leexu1244@yahoo.com)
  • Doi: https://doi.org/10.54216/NIF.040102

    Received: December 09, 2023 Accepted: June 21, 2024
    Abstract

    In this paper, we study the invertible elements (units) in the symbolic 4-plithogenic ring of integers, where we use a computational algorithm to find all units in the mentioned ring. The all-elements group of 32 symbolic 4-plithogenic ring of integers has been found and listed.

    Keywords :

    Symbolic 4-plithogenic ring , Invertible element , Group of units , Unit

    References

    [1]       Merkepci, H., and Abobala, M., " On The Symbolic 2-Plithogenic Rings", International Journal of Neutrosophic Science, 2023.

    [2]       Smarandache, F., " Introduction to the Symbolic Plithogenic Algebraic Structures (revisited)", Neutrosophic Sets and Systems, vol. 53, 2023.

    [3]       Taffach, N., and Ben Othman, K., " An Introduction to Symbolic 2-Plithogenic Modules Over Symbolic 2-Plithogenic Rings", Neutrosophic Sets and Systems, Vol 54, 2023.

    [4]       Albasheer, O., Hajjari., A., and Dalla., R., " On The Symbolic 3-Plithogenic Rings and TheirAlgebraic Properties", Neutrosophic Sets and Systems, Vol 54, 2023.

    [5]       Ben Othman, K., "On Some Algorithms For Solving Symbolic 3-Plithogenic Equations", Neoma Journal Of Mathematics and Computer Science, 2023.

    [6]       Rawashdeh, A., "An Introduction To The Symbolic 3-plithogenic Number Theory", Neoma Journal Of Mathematics and Computer Science, 2023.

    [7]       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.

    [8]       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.

    [9]       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.

    [10]    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.

    [11]    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.

    [12]    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.

    [13]    Sankari, H., and Abobala, M., " On The Algebraic Homomorphisms Between Symbolic 2-Plithogenic Rings And 2-cyclic Refined Rings", Neutrosophic Sets and Systems, 2023.

    [14]    Abobala, M., Ziena, M.B., Doewes, R.I., Hussein, Z. The Representation of Refined Neutrosophic Matrices By Refined Neutrosophic Linear Functions, International Journal of Neutrosophic Science, 2022, 19(1), pp. 342–349

    [15]    Abobala, M., On Refined Neutrosophic Matrices and Their Applications In Refined Neutrosophic Algebraic Equations, Journal Of Mathematics, Hindawi, 2021

    [16]    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, 6( 2), 37-45. DOI: https://doi.org/10.54216/IJAACI.060204

    [17]    Soueycatt, M., Charchekhandra, B., Abu Hakmeh, R., " On The Foundations Of Symbolic 5-Plithogenic Number Theory", Neutrosophic Sets and Systems, vol. 59, 2023.

    [18]    Merkepci, H., and Rawashdeh, A., " On The Symbolic 2-Plithogenic Number Theory and Integers ", Neutrosophic Sets and Systems, Vol 54, 2023.

    [19]    avier Gamboa-Cruzado, Renatto Oyague Guerra, Enrique Condor Tinoco, Guillermo Paucar-Carlos, Juan Gamarra Moreno, Warshine Barry. (2024). A Study of the 16-Plithogenic and 17-Plithogenic Square Real Matrices and Their Properties. Journal of International Journal of Neutrosophic Science, 23 ( 3 ), 63-76 (Doi   :  https://doi.org/10.54216/IJNS.230306).

    [20]    Smarandache F., and Abobala, M.,  "n-Refined Neutrosophic Vector Spaces", International Journal of Neutrosophic Science, Vol. 7, pp. 47-54. 2020.

    [21]    Abobala, M.,. "A Study of AH-Substructures in n-Refined Neutrosophic Vector Spaces", International Journal of Neutrosophic Science", Vol. 9, pp.74-85. 2020.

    [22]    Abobala, M., "On The Characterization of Maximal and Minimal Ideals In Several Neutrosophic Rings", Neutrosophic Sets and Systems, Vol. 45, 2021.

    [23]    Nader Mahmoud Taffach , Ahmed Hatip., "A Review on Symbolic 2-Plithogenic Algebraic Structures " Galoitica Journal Of Mathematical Structures and Applications, Vol.5, 2023.

    [24]    Nader Mahmoud Taffach , Ahmed Hatip.," A Brief Review on The Symbolic 2-Plithogenic Number Theory and Algebraic Equations ", Galoitica Journal Of Mathematical Structures and Applications, Vol.5, 2023.

    [25]    Abobala, M., "Neutrosophic Real Inner Product Spaces", Neutrosophic Sets and Systems, Vol. 43, 2021.

    [26]    P. Prabakaran, Bilal Abdallah, Turayeva Dinara Tulkunovna. (2024). On Certain Algebraic Properties of Symbolic 3-Plithogenic Real Square Matrices. Journal of International Journal of Neutrosophic Science, 23 ( 4 ), 350-357 (Doi   :  https://doi.org/10.54216/IJNS.230427).

    [27]    Necati Olgun. (2023). On The 15-Plithogenic Square Real Matrices. Galoitica: Journal of Mathematical Structures and Applications, 9 ( 2 ), 41-48 (Doi   :  https://doi.org/10.54216/GJMSA.090205).

    [28]   Noor Edin Rabeh, Othman Al-Basheer, Sara Sawalmeh, Rozina Ali. (2023). An Algebraic Approach to n-Plithogenic Square Matrices For 18 ≤ n ≤ 19. Journal of Neutrosophic and Fuzzy Systems, 7 ( 2 ), 08-23 (Doi   :  https://doi.org/10.54216/JNFS.070201)

    Cite This Article As :
    Xu, Lee. On the Computation of Units in Symbolic 4- Plithogenic Ring of Integers. Neutrosophic and Information Fusion, vol. , no. , 2024, pp. 06-14. DOI: https://doi.org/10.54216/NIF.040102
    Xu, L. (2024). On the Computation of Units in Symbolic 4- Plithogenic Ring of Integers. Neutrosophic and Information Fusion, (), 06-14. DOI: https://doi.org/10.54216/NIF.040102
    Xu, Lee. On the Computation of Units in Symbolic 4- Plithogenic Ring of Integers. Neutrosophic and Information Fusion , no. (2024): 06-14. DOI: https://doi.org/10.54216/NIF.040102
    Xu, L. (2024) . On the Computation of Units in Symbolic 4- Plithogenic Ring of Integers. Neutrosophic and Information Fusion , () , 06-14 . DOI: https://doi.org/10.54216/NIF.040102
    Xu L. [2024]. On the Computation of Units in Symbolic 4- Plithogenic Ring of Integers. Neutrosophic and Information Fusion. (): 06-14. DOI: https://doi.org/10.54216/NIF.040102
    Xu, L. "On the Computation of Units in Symbolic 4- Plithogenic Ring of Integers," Neutrosophic and Information Fusion, vol. , no. , pp. 06-14, 2024. DOI: https://doi.org/10.54216/NIF.040102