J-primary submodules

Abstract

Let R be a commutative ring with identity and N is a proper submodule of an R-module M. A submodule N is said to be J-primary if whenever rx ∈ N + J(M) for some r ∈ R, x ∈ M and J(M) is the Jacobson radical of M implies that either x ∈ N or . The goal of our research is to study the concept of J-primary submodules and some properties and characterizations for this class of submodules are considered.