关于强正则环的一些研究

Some Studies on Strongly Regular Rings

主要证明了下列条件等价:(1)R是强正则环;(2)R是ELT-的半素环,且对于R的每一个本质左理想L,(R/L)R是平坦模,R的每一个极大左理想或极大右理想是GW-理想;(3)R是ZC-环,R的每一个极大本质左理想是GW-理想且R的每一个单奇异左模是GP-同射模或平坦模.

In this paper,we mainly proved that the following conditions are equivalent：（1） R is a strongly regular ring;（2） R is a ELT-semi-prime ring,and for every essential left ideal L of R,（R/L）R is flat,every maximal left ideal or maximal right ideal of R is GW-ideal;（3） R is a ZC-ring,every maximal essential left ideal of R is GW-ideal and every simple singular left R-module is either GP-injective or flat.