Volume 20 , Issue 3 , PP: 115-122, 2023 | Cite this article as | XML | Html | PDF | Full Length Article
Hamiyet Merkepci 1 * , Mohammad Abobala 2
Doi: https://doi.org/10.54216/IJNS.200311
The objective of this paper is to study for the first time the algebraic properties of symbolic 2-plithogenic rings generated from the fusion of symbolic plithogenic sets with algebraic rings, where we study some of the elementary properties and substructures of symbolic 2-plithogenic rings such as AH-ideals, AH-homomorphisms, and AHS-isomorphisms. Also, the idempotency and nilpotency of symbolic 2-plithogenic elements in terms of theorems have been discussed. Besides, many examples to clarify the validity of our work have been covered.
Symbolic plithogenic set , 2-plithogenic ring , AH-ideal , AH-homomorphism
[1] Sankari, H., and Abobala, M.," AH-Homomorphisms In neutrosophic Rings and Refined Neutrosophic Rings", Neutrosophic Sets and Systems, Vol. 38, pp. 101-112, 2020.
[2] Abobala, M., "A Study Of Nil Ideals and Kothe's Conjecture In Neutrosophic Rings", International Journal of Mathematics and Mathematical Sciences, hindawi, 2021.
[3] M. Ibrahim. A. Agboola, B.Badmus and S. Akinleye. On refined Neutrosophic Vector Spaces . International Journal of Neutrosophic Science, Vol. 7, 2020, pp. 97-109.
[4] Adeleke, E.O., Agboola, A.A.A.,and Smarandache, F., "Reļ¬ned Neutrosophic Rings I", International Journal of Neutrosophic Science, Vol. 2(2), pp. 77-81. 2020.
[5] ] Smarandache, F., " n-Valued Refined Neutrosophic Logic and Its Applications in Physics", Progress in Physics, 143-146, Vol. 4, 2013.
[6] Agboola, A.A.A,. Akwu, A.D,. and Oyebo, Y.T., " Neutrosophic Groups and Subgroups", International .J .Math. Combin, Vol. 3, pp. 1-9. 2012.
[7] Smarandache, F., "Neutrosophic Set a Generalization of the Intuitionistic Fuzzy Sets", Inter. J. Pure Appl. Math., pp. 287-297. 2005.
[8] Aswad, F, M., " A Study of Neutrosophic Complex Number and Applications", Neutrosophic Knowledge, Vol. 1, 2020.
[9] Smarandache, F., and Kandasamy, V.W.B., " Finite Neutrosophic Complex Numbers",·Source: arXiv. 2011.
[10] Smarandache, F., and Ali, M., "Neutrosophic Triplet Group", Neural. Compute. Appl. 2019.
[11] Abobala, M., Hatip, A., Bal,M.," A Study Of Some Neutrosophic Clean Rings", International journal of neutrosophic science, 2022.
[12].Abobala, M., "On Some Special Substructures of Neutrosophic Rings and Their Properties", International Journal of Neutrosophic Science", Vol 4 , pp72-81, 2020.
[13] F. Smarandache, Neutrosophic Quadruple Numbers, Refined Neutrosophic Quadruple Numbers,
Absorbance Law, and the Multiplication of Neutrosophic Quadruple Numbers. In Symbolic NeutrosophicTheory, Chapter 7, pages 186-193, Europa Nova, Brussels, Belgium, 2015.
[14] F. Smarandache, Plithogeny, Plithogenic Set, Logic, Probability, and Statistics, 141 pages, Pons Editions,Brussels, Belgium, 2017. arXiv.org (Cornell University), Computer Science - Artificial Intelligence, 03Bxx:
[15] Florentin Smarandache, Physical Plithogenic Set, 71st Annual Gaseous Electronics Conference, Session LW1, Oregon Convention Center Room, Portland, Oregon, USA, November 5–9, 2018.
[16] Florentin Smarandache: Plithogenic Set, an Extension of Crisp, Fuzzy, Intuitionistic Fuzzy, and Neutrosophic Sets – Revisited, Neutrosophic Sets and Systems, vol. 21, 2018, pp. 153-166.
[17] Florentin Smarandache, Plithogenic Algebraic Structures. Chapter in “Nidus idearum Scilogs, V: joining the dots” (third version), Pons Publishing Brussels, pp. 123-125, 2019.
[18] P. K. Singh, Data with Turiyam Set for fourth dimension Quantum Information Processing. Journal of
Neutrosophic and Fuzzy Systems, Vol. 1, Issue 1, pp. 9-23, 2021.
[19] P. K. Singh, Quaternion Set for Dealing Fluctuation in Quantum Turiyam Cognition, Journal of Neutrosophic
and Fuzzy Systems, Vol. 04, No. 02, pp. 57-64, 2022.
[20].Abobala, M., "On Some Special Substructures of Refined Neutrosophic Rings", International Journal of Neutrosophic Science, Vol 5, pp59-66, 2020.
[21]. Abobala, M,. "Classical Homomorphisms Between Refined Neutrosophic Rings and Neutrosophic Rings", International Journal of Neutrosophic Science, Vol 5, pp72-75, 2020.
[22] A. Alrida Basher, Katy D. Ahmad, Rosina Ali, An Introduction to the Symbolic Turiyam Groups and AH-Substructures,,Journal of Neutrosophic and Fuzzy Systems, Vol. 03, No. 02, pp. 43-52, 2022.
[23] P. K. Singh, On the Symbolic Turiyam Rings, Journal of Neutrosophic and Fuzzy Systems, Vol. 1, No. 2, pp. 80-88, 2022.
[24] T.Chalapathi and L. Madhavi,. "Neutrosophic Boolean Rings", Neutrosophic Sets and Systems, Vol. 33,pp. 57-66, 2020.
[25] G. Shahzadi, M. Akram and A. B. Saeid, "An Application of Single-Valued Neutrosophic Sets in Medical Diagnosis," Neutrosophic Sets and Systems, vol. 18, pp. 80-88, 2017.
[26] Sarkis, M., " On The Solutions Of Fermat's Diophantine Equation In 3-refined Neutrosophic Ring of Integers", Neoma Journal of Mathematics and Computer Science, 2023.
[27] J. Anuradha and V. S, "Neutrosophic Fuzzy Hierarchical Clustering for Dengue Analysis in Sri Lanka," Neutrosophic Sets and Systems, vol. 31, pp. 179-199, 2020.
[28] Celik, M., and Olgun, N., " An Introduction To Neutrosophic Real Banach And Hillbert Spaces", Galoitica Journal Of Mathematical Structures And Applications, 2022.
[29] Celik, M., and Olgun, N., " On The Classification Of Neutrosophic Complex Inner Product Spaces", Galoitica Journal Of Mathematical Structures And Applications, 2022.
[30] Smarandache, F., " Introduction to the Symbolic Plithogenic Algebraic Structures (revisited)", Neutrosophic Sets and Systems, vol. 53, 2023.
