左理想几满乎足降链条件的本原环

On Primitive Ring with Practical Satisfaction of Descending Chain Conditions for Left Ideals

本文主要给出下述结果。(1)Ω为右本原环,A 为Ω非零理想,Ω的真含于 A 的左理想几乎满足降链条件,则Ω也为左本原环。(2)左理想几乎满足降链条件的本原环是单纯环。

The following results are obtained:(1)If Ω is a right primitive ring, A is Ω non-nil ideal and left ideals of Ω contained in A practically satisfy the descending chain condition,Ω is a left primitive ring.(2)If left ideals of Ω practically satisfy the descending chain condition,Ω is a simple ring.