Some classes of rings which are all J-reduced

Let R be a ring with identity, J(R) and Nil(R) denote the Jacobson radical and the set of all nilpotent elements of R, respectively. A ring R is called J-reduced if Nil(R)J(R)⊆. In this paper, we emphasize on reduced, SI, and 2- primal rings. These classes of rings are all J-reduced. Also, it is included some examples of such rings.

Keywords:

Nilpotent element , Jacobson radical , Reduced ring , J-reduced ring , SI-ring , 2- primal ring