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End--Prime Submodules | ||
| Ibn Al-Haitham Journal For Pure And Applied Science | ||
| Article 1, Volume 29, Issue 2, 2016, Pages 262-270 | ||
| Authors | ||
| Nuhad S. AL-Mothafar; Adwia J. Abdil -Khalik | ||
| 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. | ||
| Keywords | ||
| Prime submodules; prime submodules; end; End | ||
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