Year: 2024
Type: article
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.
Authors: Muntaha AL-Fahdawi, Majid Al-Shujairy
Institution: University of Anbar
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4406401340