关于环的内射性的一点注记

A note on injectivity of rings

设R是环,称R满足条件(P),如果存在e=e2∈R,使得(1-e)RR是半单环.给出了条件(P)下IP-内射环与自内射环、P-内射环、C2-环及QF环的等价条件.

Let R be a ring, say R satisfying the condition （P）, if there exists e=e^2∈R such that （1-e）RR is semisimple. Some equivalent conditions of IP-injective ring and self injective ring, P-injective ring, C2 -ring, QF ring are given under condition （P）.