Approximaitly Quasi-Prime Submodules and Some Related Concepts
Journal of Al-Qadisiyah for Computer Science and Mathematics,
2019, Volume 11, Issue 2, Pages 54-62
Abstract“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.
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