SF-环与强正则环  

SF-Rings and Strongly Regular Rings

作　　者：雷震[1] 

机构地区：[1]芜湖师范专科学校数学系,安徽芜湖241008

出　　处：《宁夏大学学报（自然科学版）》2004年第3期201-202,205,共3页Journal of Ningxia University(Natural Science Edition)

摘　　要：研究了满足某些条件的SF 环的正则性,得到了以下主要结论:①若R是左(或者右)SF 环,且R的所有幂 零元的左零化子是本质的左理想,则R是强正则环;②若R是左(或者右)SF 环,则R是除环当且仅当R是左一致 环.A ring R is called a left (right) SF-ring if all simple left (right) R-modules are flat. In this paper, we study the regularity of SF-rings which satisfy certain additional conditions, and prove that ①if ring R is a left(or right) SF-ring whose every left annihilator of nilpotent is a essential left ideal,then R is a strongly regular ring, ②if R is a left(or right)SF-ring,then R is a division ring if only if R is a left uniform ring.

关 键 词：强正则环 SF-环 幂零元 零化子 本质左理想 

分 类 号：O153.3[理学—数学]