On Locally S-prime and Locally S-Primary Submodules

الملخص

 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.