SF环的正则性(英文)  

On regularity of SF-rings

作　　者：潘勇[1] 

机构地区：[1]南京大学数学系

出　　处：《宝鸡文理学院学报（自然科学版）》2001年第4期259-261,共3页Journal of Baoji University of Arts and Sciences(Natural Science Edition)

摘　　要：讨论了 SF环的正则性 ,证明了如果 R是 SF环且是 ZI环 ,则 R是正则的。同时证明了 SF环 R如果满足下列三条件之一 ,则 R是强正则环 :(1 ) R是 ZI环并且每个单奇异右 (或左 ) R -模是 GP-内射的 ;(2 ) R是 SRB环并且每个单奇异右 R -模是 GP-内射的 ;(3 ) R是 2 - primal环并且每个单右 R -模是 GP-内射的。We investigate von Neumann regularity of SF-rings.It is shown that SF-ring R is regular if R is ZI ring.And it is also shown that SF-rings are strongly reqular for each of the following classes of rings:(1)strongly bounded rings whose simple singular right R-modules are GP-injective;(2)zero insertive rings whose simple singular right (or left)R-modules are GP-injective;(3)2-primal ring whose every simple right R-module is GP-injective.

关 键 词：SF环 单奇异模 GP-内射模 强正则环 ZI环 正则性 Z-primal环 

分 类 号：O153.3[理学—数学]