On Strongly Copure Flat Modules and Copure Flat Dimensions

Abstract

Let R be a left coherent ring. We first prove that a right R-module M is strongly copure flat if and only if Ext ⁱ (M, C) = 0 for all flat cotorsion right R-modules C and i ≥ 1. Then we define and investigate copure flat dimensions of left coherent rings. Finally, we give some new characterizations of n-FC rings.

Key Words:

• Copure flat dimension
• Flat dimension
• (Pre)Cover
• (Pre)Envelope
• Strongly copure cotorsion module
• Strongly copure flat module

2000 Mathematics Subject Classification:

• 16D40
• 16E10
• 16E30

ACKNOWLEDGMENTS

This research was partially supported by National Natural Science Foundation of China (No. 10771096), Natural Science Foundation of Jiangsu Province of China (No. 2008365) and Science Foundation for Young Teachers of Northeast Normal University (09QNJJ003).

Notes

Communicated by T. Albu.