主左理想几乎满足降链条件环的若干结果

Some Results of Rings Almost Satistying the Descending Chain Conditions for Principal Left Ideals

设Ω为主左理想几乎满足降链条件的环,N为Ω的质根,则Ω/N为主左理想满足降链条件的环,若再设Ω为带幂等心的亚直不可约环,则Ω为带极小单边理想的单环。

Let Ω be a ring almost satisfying the descending chain conditions for principal left ideals and N the prime radical of Ω , we prove that Ω/N is a ring satisfying the descending chain conditions for principal left ideals. Let Ω be a subdirectly irreducible ring with the heart H=H^2, we prove that if Ω almost satisfies the desceding chain conditions for principal left ideals, Ω is a simple ring with minimal one-side ideals.