Galoitica: Journal of Mathematical Structures and Applications

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Volume 12 , Issue 1 , PP: 36-43, 2025 | Cite this article as | XML | Html | PDF | Full Length Article

An Introduction to Symbolic Neutrosophic Algebras

Nader Taffach 1 * , Mohammad Al-Shiekh 2

  • 1 Department of mathematics, Idlib University, Idlib, Syria - (nader_mahmoud_taffach@idlib.edu.sy)
  • 2 Department of mathematics, Idlib University, Idlib, Syria - (mohammad_al_sheikh@idlib.edu.sy)
  • Doi: https://doi.org/10.54216/GJMSA.0120105

    Received: October 18, 2024 Revised: December 02, 2024 Accepted: January 02, 2025
    Abstract

    The objective of this paper is to study for the first time the concept of symbolic neutrosophic algebra defined over a neutrosophic ring R(I), where we derive a strict definition of this concept as an expansion of neutrosophic modules. In addition, we study some of its elementary properties such as neutrosophic subalgebras, neutrosophic homomorphisms and kernels through many theorems and mathematical proofs.

    Keywords :

    Neutrosophic ring , Neutrosophic module , Neutrosophic algebra , Neutrosophic homomorphism

    References

    [1]       F. Smarandache, "A Unifying Field in Logics: Neutrosophic Logic, Neutrosophy, Neutrosophic Set, Neutrosophic Probability," American Research Press, Rehoboth, 2003.

    [2]       J. Smith, A. Brown, and L. Johnson, "Exploring the Applications of Neutrosophic Logic in Decision-Making Processes," International Journal of Computational Intelligence Systems, vol. 15, no. 3, pp. 123-132, 2022.

    [3]       A. A. A. Agboola, "On Refined Neutrosophic Algebraic Structures," Neutrosophic Sets and Systems, vol. 10, pp. 99-101, 2015.

    [4]       V. W. B. Kandasamy and F. Smarandache, "Some Neutrosophic Algebraic Structures and Neutrosophic N-Algebraic Structures," Hexis, Phoenix, Arizona, 2006.

    [5]       A. A. A. Agboola, A. D. Akinola, and O. Y. Oyebola, "Neutrosophic Rings I," International Journal of Mathematics and Combinatorics, vol. 4, pp. 1-14, 2011.

    [6]       R. Williams and T. Davis, "Neutrosophic Sets in Data Mining: A Comprehensive Review," Journal of Data Analysis and Information Processing, vol. 10, no. 1, pp. 45-58, 2021.

    [7]       K. Thompson and M. Green, "An Overview of Neutrosophic Theory and Its Applications in Artificial Intelligence," Journal of Artificial Intelligence Research, vol. 34, pp. 101-115, 2023.

    [8]       M. Abobala, "Semi Homomorphisms and Algebraic Relations between Strong Refined Neutrosophic Modules and Strong Neutrosophic Modules," Neutrosophic Sets and Systems, vol. 39, 2021.

    [9]       R. Alhamido and M. Abobala, "AH-Substructures in Neutrosophic Modules," International Journal of Neutrosophic Science, vol. 7, pp. 79-86, 2020.

    Cite This Article As :
    Taffach, Nader. , Al-Shiekh, Mohammad. An Introduction to Symbolic Neutrosophic Algebras. Galoitica: Journal of Mathematical Structures and Applications, vol. , no. , 2025, pp. 36-43. DOI: https://doi.org/10.54216/GJMSA.0120105
    Taffach, N. Al-Shiekh, M. (2025). An Introduction to Symbolic Neutrosophic Algebras. Galoitica: Journal of Mathematical Structures and Applications, (), 36-43. DOI: https://doi.org/10.54216/GJMSA.0120105
    Taffach, Nader. Al-Shiekh, Mohammad. An Introduction to Symbolic Neutrosophic Algebras. Galoitica: Journal of Mathematical Structures and Applications , no. (2025): 36-43. DOI: https://doi.org/10.54216/GJMSA.0120105
    Taffach, N. , Al-Shiekh, M. (2025) . An Introduction to Symbolic Neutrosophic Algebras. Galoitica: Journal of Mathematical Structures and Applications , () , 36-43 . DOI: https://doi.org/10.54216/GJMSA.0120105
    Taffach N. , Al-Shiekh M. [2025]. An Introduction to Symbolic Neutrosophic Algebras. Galoitica: Journal of Mathematical Structures and Applications. (): 36-43. DOI: https://doi.org/10.54216/GJMSA.0120105
    Taffach, N. Al-Shiekh, M. "An Introduction to Symbolic Neutrosophic Algebras," Galoitica: Journal of Mathematical Structures and Applications, vol. , no. , pp. 36-43, 2025. DOI: https://doi.org/10.54216/GJMSA.0120105