SF'-环的正则性  

The regularity of SF'-rings

作　　者：方霞[1] 肖光世[1] 

机构地区：[1]南京航空航天大学理学院,江苏南京210016

出　　处：《宝鸡文理学院学报（自然科学版）》2008年第2期77-79,共3页Journal of Baoji University of Arts and Sciences(Natural Science Edition)

摘　　要：目的环R的每一个单奇异的左(右)R-模是平坦的,则称R是左(右)SF'-环,文章研究SF'-环的正则性。方法在幂等元是左半中心的和LANE-环的条件下讨论SF'-环。结果得到了SF'-环是强正则环的两个充要条件:(1)R是左SF'-环,如果R/Z(RR)是约化的,则R是强正则环;(2)R是强正则环当且仅当R是满足幂等元左半中心的左SF'-环,且R是LANE-环。结论这些结果对于解决SF-环是否是正则环有一定意义。Aim A ring R is a left （right） SF′-ring if every simple singular left （right） R-module is flat. The regularity of SF′-rings is studied. Methods SF′-rings are discussed on condition that every idempotent element is left semi-center and SF′-rings are LANE-ring. Results Two new characterizations of regular rings are given. （1） If R is a left SF′-ring and R/Z（RR） is reduced, then R is strongly regular; （2） R is strongly regular if and only if R is a left SF′-ring whose every idempotent element of R is left semi-center and is LANE-ring. Conclusion The results are helpful for the problem that SF- rings are regular rings or not.

关 键 词：强正则环 SF′-环 SF-环 

分 类 号：O153.3[理学—数学]