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Research Paper | Mathematics | Iraq | Volume 6 Issue 6, June 2017

End-?-Primary Submodules

Nuhad S. AL-Mothafar | Adwia J. AbdilKhalik

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--primary if for each EndR (M) and x M, if (x) P, then either x P + (P) or n (M) P + (P) for some nZ+. Some of the properties of this concept will be investigated. Some characterizations of end--primary submodules will be given.

Keywords: Prime submodules, Primary submodules, end--primary submodules, end--prime submodules

Edition: Volume 6 Issue 6, June 2017,

Pages: 2446 - 2450

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