摘要
文献[1]讨论双群结合环(А,Γ)的诣零性。本文把环论中相应的构造性定理推广到双群结合环,并得到:环(А,Γ)的Koethe根是具某性质的素理想的交;环(А,Γ)是Koethe半单的充要条件是它为一些Koethe半单、素环的亚直和。
The nil problem of two-group associative rings (A,Γ) is discussed in (1). In this paper, the construction theories of rings are generalized to two-group associative rings. Thus, we have: Koethe radical of the ring (A,Γ) is the intersection of some prime ideals with a certain property; if (A,Γ) is subdirect sum of some koethe semi-simple and prime rings,the ring (A,Γ) will be koethe semi-simple.
