aspg-21-1960-1791472127 20261008150847 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2023 21 4 Majid Mohammed Abed Department of Mathematics, College of Education for Pure Sciences, University Of Anbar, Anbar, Iraq Abdulsalam F. Talak Department of Mathematics, College of Education for Pure Sciences, University Of Anbar, Anbar, Iraq Firas N. Hameed Ministry of Education, General Directorate of Education in Anbar Governorate, Anbar, Iraq 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 style='mso-bidi-font-style:normal'> "Cambria Math",serif;mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font: major-bidi;mso-bidi-language:AR-IQ'>∪ I)-module; if NC(M style='mso-bidi-font-style:normal'> "Cambria Math",serif;mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font: major-bidi;mso-bidi-language:AR-IQ'>∪ I) over NC(R style='mso-bidi-font-style:normal'> "Cambria Math",serif;mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font: major-bidi;mso-bidi-language:AR-IQ'>∪ I), then NC(Z(M style='mso-bidi-font-style:normal'> "Cambria Math",serif;mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font: major-bidi;mso-bidi-language:AR-IQ'>∪ I)) ≤ NC(M style='mso-bidi-font-style:normal'> "Cambria Math",serif;mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font: major-bidi;mso-bidi-language:AR-IQ'>∪ 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. 2023 30 35 1960 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.210403 https://www.americaspg.com/journal/21/article/1960 https://www.americaspg.com/storage/91690404469.pdf