2017•Ibn AL- Haitham Journal For Pure and Applied ScienceOpen access
End ᴪ -Prime Submodules
Nuhad S. Al-Mothafar, Adwia J. Abdil Khalik
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Abstract
Let R be a commutative ring with identity and M an unitary R-module. Let (M) be the set of all submodules of M, and : (M) (M) {} be a function. We say that a proper submodule P of M is end--prime if for each EndR(M) and x M, if (x) P, then either x P + (P) or (M) P + (P). Some of the properties of this concept will be investigated. Some characterizations of end--prime submodules will be given, and we show that under some assumtions prime submodules and end--prime submodules are coincide.