两种超限幂零的关系

本文在结合环类中考察两种超限幂零的关系

Transfinite Nilpotence

For a ring R(associative)the transfinite powers R 2 α are defined as follows: R 2 0 =R,R 2 α+1 =(R 2α ) 2 ,and R 2 β =∩α<βR 2 α if β is a limit ordinal.R is said to be A-transfinite nilpotent if R 2 α =0 for some α.The transfinite powers R α are defined as follows; R 1=R,R α+1 =R αR, and R β=∩α<βR α if β is a limit ordinal.R is said to be B-transfinite nilpotent if R α =0 for some α. Theorem 3 The B-transfinite nilpotent ring R is the A-transfinite nilpotent.