n- Refined Neutrosophic of Fine Module With Some Applications

In this paper, we study and present an important concept in module theory which namely neutrosophic fine module. Fine property for modules and rings. We denote ( - module) to Fine module. Also, we investigate several facts about the relationships between fine module and - ring, projective and injective modules have a direct relationship with - module. We proved that every continuous module is - module and discrete module is also - module. Also, if has perfect property, so every guasi- projective over has fine property. We showed that every divisible module over the field is a fine module. We study a very famous property of a submodule of and we need to present some concepts that have a direct relationship to a fine module namely finitely generated (f.g.) submodule and flat modules. Finally, we proved that every cyclic module such that every submodule of it is isomorphic to summand of it , then is fine module if it has projective cover.