End-?-Primary Submodules
Journal: International Journal of Science and Research (IJSR) (Vol.6, No. 6)Publication Date: 2017-06-05
Authors : Nuhad S. AL-Mothafar; Adwia J. AbdilKhalik;
Page : 2446-2450
Keywords : Prime submodules; Primary submodules; end--primary submodules; end--prime submodules;
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.
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