Vol. 4 (08) pp. 355-361 DOI: 10.21474/IJAR01/1224

Z- PRIMESUBMODULES.

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  • Department of Mathematics, College of Science, Baghdad University, Baghdad, Iraq.
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Abstract

LetR be a commutative ring with identity and Mbe a unitary R-module, a submodulN of an R-module M is called prime if for each x?M,r?R such that rx?N implies thateither x?Nor r?[N:M]. In this paper we say that Nis a Z-prime submodule of an R-module Mif for eachx?M,f?M^*=Hom(M,R), such that f(x).x?Nimplies that either x?Norf(x)?[N:M], where [N:M]={r: r?RandrM?N}. We study also aZ-prime module in which (0) is a Z-prime submoduleinM. We give many properties of Z-prime submodule and Z-prime module.

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How to Cite This Article

Nuhad Salim Al-Mothafar and Ali Talal Husain. (2016); Z- PRIMESUBMODULES., Int. J. of Adv. Res., 4 (08), 355-361, ISSN 2320-5407. DOI: https://doi.org/10.21474/IJAR01/1224

Corresponding Author

Nuhad Salim Al-Mothafar

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