Approximaitly Prime Submodules and Some Related Concepts

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Ali Sh. Ajeel Haibat K. Mohammad Ali


In this research note approximately prime submodules is defined as a new generalization of prime submodules of unitary modules over a commutative ring with identity. A proper submodule  of an -module  is called an approximaitly prime submodule of  (for short app-prime submodule), if when ever , where , , implies that either  or . So, an ideal  of a ring  is called app-prime ideal of  if   is an app-prime submodule of -module . Several basic properties, characterizations and examples of approximaitly prime submodules were given. Furthermore, the definition of approximaitly prime radical of submodules of modules were introduced, and some of it is properties were established.

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AJEEL, Ali Sh.; MOHAMMAD ALI, Haibat K.. Approximaitly Prime Submodules and Some Related Concepts. Ibn AL- Haitham Journal For Pure and Applied Science, [S.l.], v. 32, n. 2, p. 103-113, may 2019. ISSN 2521-3407. Available at: <>. Date accessed: 18 june 2019. doi: