On Copure Projective Modules and Copure Projective Dimensions

Abstract

Let R be any ring. A right R-module M is called n-copure projective if Ext¹(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.

Key Words:

• Copure projective dimension
• n-Copure projective module
• (Pre)Cover
• (Pre)Envelope
• Strongly copure projective module

2000 Mathematics Subject Classification:

• 16D50
• 16E10
• 16E30

ACKNOWLEDGMENTS

This research was partially supported by National Natural Science Foundation of China (11071111), Natural Science Foundation of Zhejiang Province of China (Y6100173), Natural Science Foundation of Jiangsu Province of China (2008365), and by Science Foundation for Young Teachers of Northeast Normal University (09QNJJ003). The authors would like to thank the referee for the helpful comments and suggestions.

Notes

Communicated by T. Albu.