International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/524 2020 2020 Rajagiri School of Engineering and Technology, Kerala, India Binu R The paper focuses on the applications of neutrosophic set theory in the domain of classical algebraic structures, especially R-module. This study discusses some algebraic operations of neutrosophic sets of an R-moduleM, induced by the operations in M and demonstrates certain properties of the neutrosophic submodules of an R-module. The ideas of R module’s non-empty arbitrary family of neutrosophic submodules are characterized, and related outcomes are proved. The last section of this paper also derives a necessary and sufficient condition for a neutrosophic set of an R-module M. 2020 2020 118 127 10.54216/IJNS.080205 https://www.americaspg.com/articleinfo/21/show/524