A Characterization of Gorenstein Projective Modules

Abstract

In this article, we give a new characterization of Gorenstein projective modules. As applications of our result, we prove that a strongly Gorenstein projective module of countable type is Gorenstein flat, and each left R-module has a special Gorenstein projective precover whenever all projective left R-modules have finite injective dimension.

Key Words:

• Cotorsion pairs
• Gorenstein flat modules
• Gorenstein projective modules
• Strongly Gorenstein projective modules

2010 Mathematics Subject Classification:

• 16E05
• 16E30
• 16E65

ACKNOWLEDGMENTS

The authors would like to express their gratitude to Lars Winther Christensen and Nanqing Ding for helpful discussions regarding this work. The authors also would like to thank the referee for the careful reading of this article and the valuable comments.