General Results of Neutrosophic Bass-Rings

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DOI: https://doi.org/10.28924/2291-8639-24-2026-76
Published: Mar 19, 2026
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Abdulsalam F. Talak, Dunia Alawi Jarwan, Marrwa Abdulla Salih, Majid Mohammed Abed, Roslinda Nazar, General Results of Neutrosophic Bass-Rings, Int. J. Anal. Appl., 24 (2026), 76.

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

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.

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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.