?-J Ideals Of Commutative Rings

Let L(R)be the set of all ideals of a ring R,? be an expansion function of L(R).In this paper,the ?-J-ideal of a commutative ring is defined,that is,if a,b?R and ab?I?L(R)with a(?) J(R)(the Jacobson radical of R),then b??(I).More than that,some properties of?-J-ideals are discussed.At the same time,we defined the concept of primary J-submodule and described some properties of it.