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

How to Cite?: Nuhad S. AL-Mothafar, Adwia J. AbdilKhalik, "End-?-Primary Submodules", Volume 6 Issue 6, June 2017, International Journal of Science and Research (IJSR), Pages: 2446-2450, https://www.ijsr.net/getabstract.php?paperid=1061705, DOI: https://dx.doi.org/10.21275/1061705