On nil-Flat Modules, Nil-Injective and nil-Flat Dimensions

摘要

This paper give the definition of N-coherent rings, and study the rings by nil-injective modules and nil-flat modules. For an N-coherent ring R, we show that every nil-flat right R module is flat ? every nil-injective left R module is FP-injective ? every nil-injective pure nil-injective left R module is injective. Nil-injective dimension and nil-flat dimension are also studied. We show l.nil-id(R) ? n ? Ext i (R/Ra, M) = 0 for every i ? n and every a ? N (R), and every left R module ? Ext n+1(R/Ra, M) = 0 for every a ? N (R) and every R module M ? pd (R/Ra) ? n for any a ? N (R).