关于Γ-半环的Jacobson根

The purpose of this paper is to consider the Jacobson radical of a Γ-hemi-ring from the point of view of the representation theory in the ring theory. We will define the irreducible representation semimodule and the radical of a Γ-hemiring, and prove some fundamental properties of the radical which correspond to those in the ring theory. The external notion of the radical will be related to internal one, at the same time, we shall see that the radical defined in this paper coincides with the Jacobson radical and with the semiradical of the Γ-hemiring.