Volume 25 , Issue 4 , PP: 316-321, 2025 | Cite this article as | XML | Html | PDF | Full Length Article
Firas N. Hameed 1 * , Fawzi N. Hammad 2 , Majid Mohammed Abed 3
Doi: https://doi.org/10.54216/IJNS.250427
Neutrosophic set is a modern branch as a generalization of fuzzy concept. Zadeh in 1965 presented fuzzy concept and later he introduced more applications in more subjects of mathematics. On of the type branch of mathematics is fuzzy algebra. In this work, we present and clarify several results of several modules, which has zero-kernel, and zero homomorphism in neutrosophic theory. The aim modules are mnonoform and small monoform modules. Several concepts have been studied in this paper like Quasi-dedekind and uniform modules. We proved that if ( ( )) is a module over neutrosophic ring ( ). If ) is a directed sum of simple submodules an is monoform, then ) is monoform module. Also, if 𝒯) is a semi simple ring and 𝒯) is a 𝒯)-module, so 𝒯) is small and satisfies all conditions of monoform with Q-dedekind property. On the other hand, let be an R-module. is a neutrosophic modules and generated by and . So, is a weak neutrosophic. Finally, we presented more results, examples and properties about the topic with new results in neutrosophic algebra.
Neutrosophic module , Neutrosophic ring , Uniform module , Quasi-dedekind module , Small module
[1] M. M. Abed, "On Indeterminacy (Neutrosophic) of Hollow Modules," Iraqi Journal of Science, vol. 63, no. 6, pp. 2650-2655, 2022.
[2] J. M. Zelmanowitze, "An Extension of the Jacobson Density Theorem," Bull. Amer. Math. Soc., vol. 82, no. 4, pp. 551-553, 1976.
[3] Y. Tiraş and M. Alkan, "Prime Modules and Submodules," Commun. Algebra, vol. 31, no. 11, pp. 5253–5261, 2003.
[4] Kamal and A. M. Menshawy, "Annihilator Conditions CS-modules," Int. J. Math. Math. Sci., vol. 50, pp. 3195-3202, 2003.
[5] Faith, Lectures on Injective Modules and Quotient Rings, Springer-Verlag, Berlin, Heidelberg, New York, 1967.
[6] M. M. Abed, "A new view of closed-CS-module," Italian Journal of Pure and Applied Mathematics, no. 43, pp. 65-72, 2020.
[7] Y. B. Jun, F. Smarandache, and H. Bordbar, "Neutrosophic N-structures applied to BCK/BCI-algebras," Information, vol. 8, no. 4, pp. 128, 2017.
[8] M. Abed, D. A. Jarwan, and M. A. Salih, "On Neutrosophic Relations in Group Theory," Int. J. Math., Stat., and Comput. Sci., vol. 1, pp. 48–52, 2023.
[9] V. Cetkin, B. P. Varol, and H. Aygün, "On neutrosophic submodules of a module," Hacettepe Journal of Mathematics and Statistics, vol. 46, no. 5, pp. 791-799, 2017.
[10] M. Abodala, "Small Homomorphism and Algebraic Relations between Strong Refined Neutrosophic Modules and Strong Neutrosophic Submodules," Neutrosophic Sets and Systems, vol. 39, pp. 1-8, 2021.
[11] V. Cetkin, B. P. Varol, and H. Aygün, "On neutrosophic submodules of a module," Hacettepe Journal of Mathematics and Statistics, vol. 46, no. 5, pp. 791-799, 2017.
[12] A. R. Ali and S. H. Zail, "On the Structure of Neutrosophic Modules and Their Applications," Journal of Mathematical Structures and Applications, vol. 10, no. 4, pp. 1-12, 2021.
[13] A. Tuganbaev, "Multiplication Modules," Journal of Mathematical Sciences, vol. 123, no. 2, pp. 3837-3860, 2004.
[14] S. H. Zail, M. M. Abed, and A. S. Faisal, "On neutrosophic BCK-algebra and Ω-BCK-algebra," Int. J. Neutrosophic Sci., vol. 19, no. 3, pp. 8-15, 2022.
[15] F. F. Kareem and M. M. Abed, "Generalizations of Fuzzy k-ideals in a KU-algebra with semigroup," Journal of Physics: Conference Series, vol. 1879, pp. 022108, 2021.
[16] E. A. Naim and A. R. Mehdi, "On gs-pseudo-injective modules," Journal of Discrete Mathematical Sciences and Cryptography, vol. 25, no. 5, pp. 1535–1545, 2022. [Online]. Available: https://doi.org/10.1080/09720529.2022.2082724.
[17] M. Fujita and M. Kageyama, "Quasi-quadratic modules in pseudo-valuation domain," arXiv preprint arXiv: 2310.04116, Oct. 2023. [Online]. Available: https://arxiv.org/abs/2310.04116.
