环上广义逆包含性质的一个注记

A Note on Inclusion Properties of Generalized Inverses in a Ring

主要讨论了环上广义逆的包含性质。证明了对于幂等自反环中的两个正则元素a和b,a=b当且仅当a{1}=b{1}当且仅当a{1,2}■b{1,2}。

In this article,we investigate inclusion properties in a ring.It is proven that for two regular elements a and b of an idempotent reflexive ring R,a=b if and only if a{1}=b{1}if and only if a{1,2}■b{1,2}.