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 is an element of N + J(M) for some r is an element of R, x is an element of M and J(M) is the Jacobson radical of M implies that either x is an element of N or r is an element of root[N:M] = [s is an element of R; s(n) M subset of N for some n is an element of Z(+)]. 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.
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