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

Lee

doi:https://doi.org/10.54216/NIF.040102

Full Length Article

Volume 4 • Issue 1 • PP: 06-14 • 2024

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

Lee Xu ^1*

mail

¹University of Chinese Academy of Sciences, CAS, Mathematics Department, Beijing, China

* Corresponding Author.

DOI https://doi.org/10.54216/NIF.040102

format_quote Cite this article

verified

Open Access & Copyright

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

View PDF open_in_new

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

Choose your preferred format

format_quote

Xu, Lee. "On the Computation of Units in Symbolic 4- Plithogenic Ring of Integers." Neutrosophic and Information Fusion, vol. Volume 4, no. Issue 1, 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, Volume 4(Issue 1), 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 Volume 4, no. Issue 1 (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, Volume 4(Issue 1), pp. 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. 2024;Volume 4(Issue 1):06-14. DOI: https://doi.org/10.54216/NIF.040102

L. Xu, "On the Computation of Units in Symbolic 4- Plithogenic Ring of Integers," Neutrosophic and Information Fusion, vol. Volume 4, no. Issue 1, pp. 06-14, 2024. DOI: https://doi.org/10.54216/NIF.040102

policy

Publisher's Note

The statements, opinions, and data presented in this article are solely those of the author(s) and do not necessarily represent those of ASPG, the journal, or its editors. ASPG and the editors disclaim responsibility for any harm arising from the use of any ideas, methods, instructions, or products described in this article, to the fullest extent permitted by applicable law.

Digital Archive Ready