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n- Refined Neutrosophic of Fine Module With Some Applications | ||
| Journal of University of Anbar for Pure Science | ||
| Volume 18, Issue 2, December 2024, Pages 257-264 PDF (645.16 K) | ||
| Document Type: Review Paper | ||
| DOI: 10.37652/juaps.2024.147949.1222 | ||
| Authors | ||
| Muntaha Jaafer AL-Fahdawi* 1; Majid Mohammed Al-Shujairy2 | ||
| 1Department of mathematics, College of Education for pure Sciences, University Of Anbar | ||
| 2Department of mathematics, College of Education for pure Sciences, University of Anbar, Iraq | ||
| Abstract | ||
| Abstract: 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. | ||
| Keywords | ||
| Fine ring; Neutrosophic set; Neutrosophic module; Flat module; Injective module | ||
| References | ||
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