关于一类主左理想几乎满足降链条件环的结构

On Rings Almost Satisfying the Desceding ChainConditions for Principal Left Ideals

本文推广了ГЕРЧИКОВ和郭元春的结果.

Let Ω be ring almost satisfying DCC for principal left ideals, we prove: if Ω satisfes CM: each nonzero ideal of Ω has a non -nilpotent centrical element x, Ωis a regular and it's minimal ideals are simple Artinian ring; Ω is a direct sum of simple Artinian rings if and only if Ω satisfies CM and principal left ideals of Ω almost satis-fy DCC.