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Research Paper | Mathematics | Iraq | Volume 6 Issue 4, April 2017 | Popularity: 6.1 / 10

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?-Primary Submodules

Nuhad S.AL-Mothafar, Adwia J.Abdil.Al-Khalik

Abstract: Let R be a commutative ring with identity and M be a unitary R-module. Let (M) be the set of all submodules of M, and (M) (M) {} be a function. We say that a proper submoduleP of M is -primary if for each r R and x M, if rx P, then either x P + (P) orr^n M P + (P) for some nZ+. Some of the properties of this concept will be investigated. Some characterizations of -primesubmodules will be given, and we show that under some assumptions primesubmodules and -primarysubmodules are coincide.

Keywords: Prime submodule, Primary submodules, -primesubmodules

Edition: Volume 6 Issue 4, April 2017

Pages: 1115 - 1120

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