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, Ali Sh.; MOHAMMAD ALI, Haibat K.. Approximaitly Semi-Prime Submodules and Some Related Concepts. Ibn AL- Haitham Journal For Pure and Applied Science, [S.l.], v. 32, n. 3, p. 117-128, sep. 2019. ISSN 2521-3407. Available at: <>. Date accessed: 28 may 2020. doi: