Journal of Neutrosophic and Fuzzy Systems JNFS 2771-6449 2771-6430 10.54216/JNFS https://www.americaspg.com/journals/show/2813 2021 2021 University of Chinese Academy of Sciences, CAS, Mathematics Department, Beijing, China Lee Lee Abu Dhabi University, Abu Dhabi, UAE Maretta Sarkis Mutah University, Faculty of Science, Jordan Ammar Rawashdeh Mutah University, Faculty of Science, Jordan Ahmad Khaldi The ring of n-cyclic refined neutrosophic integers is a logical extension of the integer ring Z based on a special multiplication operation defined between the indeterminacy algebraic elements. In this paper, we provide a full description of the 4-cyclic refined neutrosophic integer roots of unity, where we prove that for odd values of n we get exactly two different solutions. For even values of n, we get exactly 15 different solutions. On the other hand, we characterize the m-cyclic refined neutrosophic modulo integers rings and present many of their algebraic properties based on neutrosophic homomorphisms and substructures. 2024 2024 38 48 10.54216/JNFS.080205 https://www.americaspg.com/articleinfo/24/show/2813