正则环与YJ内射模

REGULAR RINGS AND YJ INJECTIVE MODULES

借助 YJ内射模刻画了正则环 ,在 R满足元素右零因子幂条件下 ,环 R为正则环当且仅当每个循环右 R 模为 YJ内射模当且仅当环 R的每个本质右理想为 YJ内射模 ;另一方面 ,当 R满足特殊右零化子升链条件时 ,R为正则环当且仅当 R为半本原右 YJ内射环当且仅当 R为右非奇异的右 YJ内射环 .

This papercharactersregularringswith the aid of YJinjective modules.When R satisfies elementrightzero divison power,ring R is regularity if and only if every cyclicright R-module is YJ injective module if and only if every essential rightideal of R is YJinjective module. On the other hand,when R satisfiesacc of special rightannihilator,R is regularring if and only if R issemiprim- itive right YJinjective ring if and only if R is rightnonsingular right YJinjective ring.