Approximaitly Semi-Prime Submodules and Some Related Concepts

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Ali Sh. Ajeel
Haibat K. Mohammad ali


    We introduce in this paper the concept of approximaitly semi-prime submodules of unitary left -module  over a commutative ring  with identity as a generalization of a prime submodules and semi-prime submodules, also generalization of quasi-prime submodules and approximaitly prime submodules. Various basic properties of an approximaitly semi-prime submodules are discussed, where a proper submodule  of an -module  is called an approximaitly semi-prime submodule of  , if whenever , where ,  and , implies that . Furthermore the behaviors of approximaitly semi-prime submodule in some classes of modules are studied. On the other hand several characterizations of this concept are introduced.

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Ajeel, A. S., & Mohammad ali, H. K. (2019). Approximaitly Semi-Prime Submodules and Some Related Concepts. Ibn AL- Haitham Journal For Pure and Applied Sciences, 32(3), 117–128.