On the Radicals Determined by the Class of the SimpleΓ-rings with Unity

Abstract:

      In the radical theory of the associative rings, it is known that the upper radical determined by the class of the simple rings With unity is Brown-McCoy radical. In this paper, we study this problem for Γ- rings. The upper radicals determined by the classed of the sample Γ- rings with unity become eight different radicals owing to the complexity of the unity in Γ-rings. The relations among these eight radicals are expounded. We also establish the relations between these radicals and other radicals of Γ-rings.