ON COPURE PROJECTIVE MODULES AND COPURE PROJECTIVE DIMENSIONS

Let R be any ring. A right R-module M is called n-copure projective if Ext(1) (M, N) = 0 for any right R-module N with fd(N) <= n, and M is said to be strongly copure projective if Ext(i) (M, F) = 0 for all flat right R-modules F and all i >= 1. In this article, firstly, we present some general properties of n-copure projective modules and strongly copure projective modules. Then we define and investigate copure projective dimensions of modules and rings. Finally, more properties and applications of n-copure projective modules, strongly copure projective modules and copure projective dimensions are given over coherent rings with finite self-FP-injective dimension.