THE DUAL OF THE NOTIONS n-SUBMODULES AND J-SUBMODULES

چکیده مقاله

Let R be a commutative ring with identity and M be an R-module. A proper submodule N of M is called an n-submodule if for a ∈ R, m ∈ M, am ∈ N with a ∈ √pAnn_R(M), implies m ∈ N. A proper submodule N of M is called a J-submodule of M if for a ∈ R and m ∈ M, whenever am ∈ N and a 6∈ (J(R)M: M), then m ∈ N. The aim of this paper is to introduce and investigate the dual notions of n-submodules and J-submodules of M. Copyright © Deanship of Research and Graduate Studies, Yarmouk University, Irbid, Jordan.