On Locally S-prime and Locally S-Primary Submodules

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Adil Kadir Jabbar
Payman Mahmood Hamaali
Abdullah M. Abdul-Jabbar


 Throughout this article, we present locally prime, locally primary and locally S-semiprime submodules, as generalizations of prime, primary and semiprime submodules respectively. We investigate some properties and characterizations of these modules. For a multiplication module, the concepts of locally primary and locally primary are equivalent. Finally, we give the following result, if  is multiplication module, then  is locally primary submodule, if there exists a locally primary ideal of  such that  and . We provided that, every locally semiprime submodule of multiplication module is the intersection of some locally prime submodule.


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How to Cite
A. K. Jabbar, P. M. Hamaali, and A. M. Abdul-Jabbar, “On Locally S-prime and Locally S-Primary Submodules”, JUBPAS, vol. 27, no. 3, pp. 165-177, Jun. 2019.