Abel正则球与完全正则半群

Abelian Regular Rings And Completely Regular Semigroups

本文分别讨论了关于结合环和半群的二个定理，并且由结合环的这二个定理推出了如下准则：结合环Ｒ是Ａｂｅｌ正则的，当且仅当Ｒ的每个拟理想是正则环．

In this paper,we prove two theorems for an associative ring and a semigroup respectively,From the theorems for an associative ring, we imply the following criterion:An associatve ring R is Abelian regular if and only if every qusi-ideal Q of R is a regular ring.