摘要
本文中,我们证明了如下主要结果: 1 如果R是左P-内射环,R又是半素的,且L是R中的极大左零化子,那末L是R的极大左理想,且存在e=e^2∈R使L=Re。2 如果R是左P-内射素环,且有极大左零化子,那末R是左、右本原环。3 设R是左自内射环,那末R是正则环当且仅当对任意本质左理想L,R/L是左P-内射模。4 如果R是强左P-内射环,那末R/Z是正则环。
In this paper, we prove the following results:
1. If R is a left p-injective ring, R is semiprime, and L is a maximal left annihilator in R, then L is a maximal left ideal of R, and there exists e=e^2 ∈R such that L=Re.
2. If R is a left p-injective prime ring, and R has a maximal left annihilator, then R is a left and right primitive ring.
3. Let R be a left self-injcetive ring, then R is regular if and only if for any essential left ideal L, R/L is a left p-injective module.
4. If R is a strongly left p-irtjective ring then R/Z is a regular ring.
关键词
P-内射环
正则环
P-内射模
Von Neumann regular ring, P-injective module, P-injective ring, Strongly p-injective ring.
