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

中文关键词:  Γ－环  单位元  特殊类  上根

英文关键词:Γ-ring  unity  specisl class  upperadical.

中文摘要:

      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．

英文摘要:

      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.