International Journal of Analysis and Applications ISSN 2291-8639 (Online)

Research Article

General Results of Neutrosophic Bass-Rings

  • Abdulsalam F. Talak*
  • Dunia Alawi Jarwan
  • Marrwa Abdulla Salih
  • Majid Mohammed Abed
  • Roslinda Nazar

    * Corresponding author

    Abstract

    In this paper, we study and present a new view of Neutrosophic Bass-ring (N- Bass-ring) and neutrosophic of Semi-Bass ring. Bass-ring means; if any module M of R has max- submodule. One of the important results of Nstrongly Bass -ring is, if M is a N- V-module, R is N- strongly Bass-ring. We proved the if (M∪I) is N- V-module, (R∪I) is a N- S-Bass- ring. Also, if (N∪I) = (J∪I)(M∪I) over a N- Boolean ring, then every (N∪I) ≤ (M(I) is a Nsemi-maximal and so (M∪I) is N- semi-Bass ring. Finally, some properties and more new results have been presented.

    How to Cite

    A. F. Talak, D. A. Jarwan, M. A. Salih, M. M. Abed, R. Nazar, General Results of Neutrosophic Bass-Rings, Int. J. Anal. Appl. 24 (2026), 76. https://doi.org/10.28924/2291-8639-24-2026-76

    BibTeX
    @article{Talak2026,
  author  = {Talak, Abdulsalam F. and Jarwan, Dunia Alawi and Salih, Marrwa Abdulla and Abed, Majid Mohammed and Nazar, Roslinda},
  title   = {General Results of Neutrosophic Bass-Rings},
  journal = {Int. J. Anal. Appl.},
  volume  = {24},
  year    = {2026},
  pages   = {76},
  doi     = {10.28924/2291-8639-24-2026-76}
}

    References

    • [1] L. Zadeh, Fuzzy Sets, Inf. Control. 8 (1965), 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X.
    • [2] M. Abobala, Semi Homomorphisms and Algebraic Relations Between Strong Refined Neutrosophic Modules and Strong Neutrosophic Modules, Neutrosophic Sets Syst. 39 (2021), 107–119.
    • [3] F. Al-Sharqi, A. Al-Quran, M.U. Romdhini, Decision-Making Techniques Based on Similarity Measures of Possibility Interval Fuzzy Soft Environment, Iraqi J. Comput. Sci. Math. (2023), 18–29. https://doi.org/10.52866/ijcsm.2023.04.04.003.
    • [4] F. Smarandache, Neutrosophy: Neutrosophic Probability, Set, and Logic: Analytic Synthesis \& Synthetic Analysis, American Research Press, 1998.
    • [5] F. Smarandache, M. Ali, Neutrosophic Triplet Group, Neural Comput. Appl. 29 (2016), 595–601. https://doi.org/10.1007/s00521-016-2535-x.
    • [6] K.W.B. Vasatha, F. Smarandache, Some Neutrosophic Algebra Structures and Neutrosophic N-Algebraic Structures, Hexis, Church Rock, 2006.
    • [7] D.A. Jarwan, M.M. Abed, Applications of Neutrosophic Rings Whose Elements Are Regular, J. Discret. Math. Sci. Cryptogr. 27 (2024), 1599–1604. https://doi.org/10.47974/JDMSC-1943.
    • [8] M.M. Abed, On Indeterminacy (Neutrosophic ) of Hollow Modules, Iraqi J. Sci. (2022), 2650–2655. https://doi.org/10.24996/ijs.2022.63.6.30.
    • [9] T. Chalapathi, L. Madhavi, Neutrosophic Boolean Rings, Neutrosophic Sets Syst. 33 (2020), 57–66.
    • [10] F.F. Kareem, M.M. Abed, Generalizations of Fuzzy K-Ideals in a Ku-Algebra with Semigroup, J. Phys.: Conf. Ser. 1879 (2021), 022108. https://doi.org/10.1088/1742-6596/1879/2/022108.
    • [11] M.M. Abed, F. Al-Sharqi, S.H. Zail, Injective Modules, Projective Modules and Their Relationships to Some Rings, AIP Conf. Proc. 2472 (2022), 030002. https://doi.org/10.1063/5.0093155.
    • [12] M.M. Abed, A.F. Talak, F.N. Hameed, An Approach to Singular Modules by Indeterminacy Concept, Int. J. Neutrosophic Sci. 21 (2023), 30–35. https://doi.org/10.54216/IJNS.210403.