A GENERALIZATION OF REFLEXIVE RINGS

We introduce a class of rings which is a generalization of reflexive rings and J-reversible rings. Let R be a ring with identity and J(R) denote the Jacobson radical of R. A ring R is called J-reflexive if for any a, b is an element of R, aRb = 0 implies bRa subset of J(R). We give some characterizations of a J-reflexive ring. We prove that some results of reflexive rings can be extended to J-reflexive rings for this general setting. We conclude some relations between J-reflexive rings and some related rings. We investigate some extensions of a ring which satisfies the J-reflexive property and we show that the J-reflexive property is Morita invariant.