Al-Qadisiyah UniversityJournal of Al-Qadisiyah for Computer Science and Mathematics2074-020411220190828Approximaitly Quasi-Prime Submodules and Some Related Concepts5462162579ENHaibat K. Mohammadali Ali Sh. Ajeel Journal Article20190801“Let R be a commutative ring with identity and B is a left unitary R-module. A proper submodule E of B is called a quasi-prime submodule, if whenever rsb∈E, where r,s∈R, b∈B implies that either rb∈E or sb∈E”. As a generalization of a quasi-prime submodules, in this paper we introduce the concept of approximaitly quasi-prime submodules, where a proper submodule E of B is an approximaitly quasi-prime submodule, if whenever rsb∈E, where r,s∈R, b∈B implies that either rb∈E+soc(B) or sb∈E+soc(B), where soc(B) is the intersection of all essential submodules of B. Many basic properties, characterization and examples of this concept are given. Furthermore, we study the behavior of approximaitly quasi-prime submodules under R-homomorphisms. Finally, we introduced characterizations of approximaitly quasi-prime submodule in class of multiplication modules.<p>https://csm.iraqjournals.com/article_162579_4fe4543cad3356aeff2de84439985f51.pdf