On slightly P-coherent rings

摘要

A ring R is called left slightly P-coherent if C is P-injective, for every left R-module exact sequence 0ABC0 with A and B P-injective. The properties of slightly P-coherent rings and several examples are studied to show that left slightly P-coherent rings fall in between left P-coherent rings and left strongly P-coherent rings. In terms of some derived functors, some homological dimensions over these rings are investigated. As applications, some new characterizations of p.p.rings are given.