A GENERALIZATION OF J -QUASIPOLAR RINGS.

In this paper we introduce a class of quasipolar rings which is a generalization of J -quasipolar rings. Let R be a ring with identity. An element a ϵ 2 R is called 1-quasipolar if there exists p2 = p ϵ comm2(a) such that a + p is contained in δ(R), and the ring R is called δ-quasipolar if every element of R is δ-quasipolar. We use 1-quasipolar rings to extend some results of J-quasipolar rings. Then some of the main results of J-quasipolar rings are special cases of our results for this general setting. We give many characterizations and investigate general properties of 1-quasipolar rings. [ABSTRACT FROM AUTHOR]