有幺单Γ－环类所确定的上根

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

结合环根论中由具有单位元的单环类所确定的上根就是Ｂｒｏｗｎ－ＭｃＣｏｙ根．本文指出在Γ－环中，鉴于Γ－环单位元的复杂性质使得有幺单Γ－环类确定的上根演变成８个，进而研究了这些根之间及这些根与Γ－环其它根之间的大小关系．

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 - rings. The upper radicals determined by the classed of the sample - rings with unity become eight different radicals owing to the complexity of the unity in -rings. The relations among these eight radicals are expounded. We also establish the relations between these radicals and other radicals of - rings.