摘要
利用ZC-环和自-内射环的性质来刻画强正则环.证明了下列结果:1设R是ZC-环,下列条件等价:(1)R是强正则环;(2)R的每一个极大本质左理想是GP-内射的;(3)R中存在一个忠实左R-模K,使得当k∈K且l(k)本质时,l(k)是GP-内射的.2设R是ELT-环,且对于R的每一个本质左理想M,[R/M]R是平坦模,R的每一个补左理想是GW-理想,如果R是左MI-环,那么R是左自-内射强正则环.
This paper characterizes strongly regular rings via ZC-ring and self-injective rings. The following results are proven. 1 Let R is ZC-ring, then the following conditions are equivalent. （1） R is a strongly regular ring; （2） Every maximal essential left ideal of R is GP-injective; （3） R contains a left R-module K, such that while k∈K and l（k） is essential, l（k） is GP-injective. 2 Let R he a ELT-ring, and for every essential left ideal M of R,（R/M）R be flat and every complement left ideal of R be GW-ideal, if R is a left M/-ring, then R is a left self-inJective strongly regular ring.
出处
《滁州学院学报》
2009年第2期46-48,共3页
Journal of Chuzhou University
基金
安徽省教育厅自然科学研究重点项目(KJ2008A206)
