关于Weaker Γ_N-环

ON THE WEAKER Г_N-RING

本文定义了Weaker Γ_N-环,论证了在这个环M中必有强诣零根N,但M/N未必强诣零半单,故定义了B-诣零根N_B,M/N_B是强诣零半单的,最后给出了强诣零半单Weaker Γ_N-环的结构定理.

In this paper, we defined the weaker Γ_N-ring, and proved that there exits a strongly nil radical N in any weaker Γ_N-ring M. Because M/N is not necessarily strongly nil semi-simple, we then defined B-nil radical N_B, such that M/N_B is strongly nil semi-sinple, Finally, the sture theorem of strongly nil semi-simple weaker Γ_N-ring is proved.