On locally S−prime and locally S−primary submodules

الملخص EN

Throughout this article, we present locally S−prime, locally S −primary and locally S-semiprime submodules, as generalizations of S −prime, S −primary and S −semiprime submodules respectively.

We investigate some properties and characterizations of these modules.

For a multiplication module, the concepts of P(N) −locally primary and locally S −primary are equivalent.

Finally, we give the following result, if M is multiplication module, then K is locally primary submodule, if there exists a P(N) −locally primary ideal of R such that K = IM and M ≠ IM.

We provided that, every locally S −semiprime submodule of multiplication module is the intersection of some locally S −prime submodule.