由环的幂零性所确定的根

THE RADICALS DETERMINED BY NILPOTENCY OF RINGS

结合环中的环的幂零性不是根性质．为此，本文将结合环中的幂零理想概念扩展为次拟幂零理想和拟幂零理想，定义次拟幂零根ＳＮ和拟幂零根ＱＮ，证明它们均为Ａｍｉｔｓｕｒ－Ｋｕｒｏｓｈ根，且二者相等．进一步，我们给出了ＱＮ－半单环的构造命题和ＱＮ－根的模刻划．

In this paper, the concepts of subquasi nilpotent ideal and Quasi nilpotent ideal as extention of the notion of nilpotent ideal are introduced in the class of associative rings, the definitions of subquasi nilpotent radical and Quasi nilpotent radical are given and they are proved being Amitsur Kurosh radical and being equal. Moreover, the structure theorem of semisimple ring and module characterization for Quqsi nilpotent radical are represented respectively.