Volume 21 , Issue 4 , PP: 30-35, 2023 | Cite this article as | XML | Html | PDF | Full Length Article
Majid Mohammed Abed 1 * , Abdulsalam F. Talak 2 , Firas N. Hameed 3
Doi: https://doi.org/10.54216/IJNS.210403
In this article, we characterize a singular module and present several new strong relationships with neutrosophic (NC) properties. Some properties and characterizations neutrosophic of singular modules are given. Also, different basic results about these modules are considered. Moreover; for a (R I)-module; if NC(M I) over NC(R I), then NC(Z(M I)) ≤ NC(M I). Any neutrosophic simple module is either nonsingular or singular. On the other hand, if NC(RUI) has no zero divisors then NC(Z(MUI)) = NC(T(MUI)) where NC(T(MUI)) is a neutrosophic torsion module. Finally, some definitions and properties of neutrosophic singular module have been presented in this article.
Singular module , Free module Annihilator module , Neutrosophic ring , Neutrosophic submodule.
[1] Smarandache F. A Unifying Field in Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability, American Research Press: Rehoboth, NM, 1999.
[2] L. A. Zadeh, Fuzzy sets, Information and control, 8, 338-353, (1965).
[3] A. A. Salama and S. A. Alblowi, Neutrosophic set and neutrosophic topological spaces, IOSR Journal of Mathematics, 3 (4), 31-35, (2012).
[4] F. Al-Sharqi, Y. Al-Qudah and N. Alotaibi, Decision-making techniques based on similarity measures of possibility neutrosophic soft expert sets. Neutrosophic Sets and Systems, 55(1) (2023), 358-382.
[5] A. Al-Quran, F. Al-Sharqi, K. Ullah, M. U. Romdhini, M. Balti and M. Alomai, Bipolar fuzzy hypersoft set and its application in decision making, International Journal of Neutrosophic Science, vol. 20, no. 4, pp. 65-77, 2023.
[6] Kandasamy, W. V., & Smarandache, F. (2004). Basic neutrosophic algebraic structures and their application to fuzzy and neutrosophic models (Vol. 4). Infinite Study.
[7] Mohammed Abed, M., Hassan, N., & Al-Sharqi, F. (2022). On Neutrosophic Multiplication Module.Neutrosophic Sets and Systems, 49(1), 12 [8] Abed, M., Al-Jumaili, A. F., Al-Sharqi, F. G. Some mathematical Structures in topological group. J. Algab. Appl. Math., 2018, 16(2), 99-117.
[9] F. Al-Sharqi, A. G. Ahmad, A. Al Quran, Mapping on interval complex neutrosophic soft sets, International Journal of Neutrosophic Science, vol.19(4), pp.77-85, 2022.
[10] A. Al Quran, A. G. Ahmad, F. Al-Sharqi, A. Lutfi, Q-Complex Neutrosophic Set, International Journal of Neutrosophic Science, vol. 20(2), pp.08-19, 2023.
[11] Jumaili, A. M. A., Abed, M. M., Al-sharqi, F. G. Other new types of Mappings with Strongly Closed Graphs in Topological spaces via e-θ and δ-β-θ-open sets. J. Phys. Conf. Ser., 2019, 1234, 012101.
[12] R. K. Al-Hamido, A new neutrosophic algebraic structures. Journal of Computational and cognitive Engineering, p. 5, 2022
[13] S. H. Zail, M. M. Abed and F. AL-Sharqi, Neutrosophic BCK-algebra and Ω-BCK-algebra.International Journal of Neutrosophic Science, vol. 19, no. 3, pp. 08-15, 2022 .
[14] Al-Sharqi, F. G., Abed, M. M., Mhassin, A. A. On Polish Groups and their Applications. J. Eng. Appl. Sci., 2018, 13(18), 7533-7536.
[15] F. Al-Sharqi, M. U. Romdhini, A. Al-Quran, Group decision-making based on aggregation operator and score function of Q-neutrosophic soft matrix, Journal of Intelligent and Fuzzy Systems, vol. 45, pp.305–321, 2023.
[16] F. Al-Sharqi, A.G. Ahmad, A. Al-Quran, Fuzzy parameterized-interval complex neutrosophic soft sets and their applications under uncertainty, Journal of Intelligent and Fuzzy Systems, vol. 44, pp.1453–1477, 2023. [17] Abed, M. M. (2020). A new view of closed-CS-module. Italian Journal of Pure and Applied Mathematics, 43, 65-72.
[18] Z. A. El-Bast, and P. P. Smith, "Multiplication Module", Comm. In Algebra, 16, 755-770, 1988.
[19] K. Saeho, "On Faithful Multiplication Modules", A Thesis Approved in Partial Fulfilment of the Requirements for The Degree of Master of Science in Mathematics, Thaksin University, 201
[20] F. Kach, "Modules and Rings", Acad, Press., London, 1982.
