含k-布尔环的半单类的结构定理

The structure theorem of semi-simple classes containing k-Boolean rings

借助给出环的超裂零扩张的定义的手法,对遗传根的半单类的结构进行了研究,主要得出含k-布尔环的半单类的结构定理,证明了若遗传根的半单类S_R包含所有的k-布尔环(k是某个固定不变的整数)以及所有零环,而且S_R对k-布尔理想保持同态闭,则S_R包含所有布尔环。

The structure of semi-simple classes of hereditary radicals is studied by methods of super split-null extensions in rings. It is shown that if the semi-simple class of hereditary radicals contains all k-boolean rings and null rings and keeps morphisms closed for k-boolean ideals, then it contains all boolean rings.