δ-J Ideals Of Commutative Rings

Let L（R）be the set of all ideals of a ring R,δ be an expansion function of L（R）.In this paper,the δ-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∈δ（I）.More than that,some properties ofδ-J-ideals are discussed.At the same time,we defined the concept of primary J-submodule and described some properties of it.