وارون پذیری مدول های ضربی

throughout this dissertation r is a commutative ring with identity and m is a unitary r-module. in this dissertation we investigate submodules of multiplication , prufer and dedekind modules. we also stat the equivalent conditions for which is ring , wher l is a submodule of afaithful multiplication prufer module. we introduce the concept of integrally closed modules and show that faithful multiplication valuation modules and hence faithful multiplication prufer modules over a integral domain r are integrally closed. we proved that if r is an integral domain and m is faithful multiplication r-module and n is finitely generated submodules of m, then , where . finally we investigate the relation between afinitely generated torsion free dedekind module m over a domin r and prime submodules of the -module m, where .