Weakly J-submodules of modules over commutative rings

Abstract

Let R be a commutative ring with identity and M be a unitary R-module. By J(R), we denote the Jacobson radical of R. The purpose of this paper is to introduce the concept of weakly J-submodules generalizing J-submodules. We call a proper submodule N of M a weakly J-submodule if whenever 0 &NOTEQUexpressionL; rm is an element of N for r is an element of R and m is an element of M, then r is an element of (J(R)M : M) or m is an element of N. Various properties and characterizations of weakly J- submodules are investigated especially in the case of multiplication modules.