A note on Gorenstein projective modules

ABSTRACT

In this note, it is proven that if R is a right noetherian ring with ${id}_{R^o}R<\infty$ and ${Ext}_R^{i\ge 1}(M,F)=0$ for any left R-module F with finite flat dimension, then M is Gorenstein projective; if R is a left noetherian ring with id_RR<∞ and M is a Gorenstein projective left R-module, then ${Ext}_R^{i\ge 1}(M,F)=0$ for any left R-module F with finite flat dimension.

KEYWORDS:

• Cover
• envelope
• Gorenstein projective module

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 16E05
• 16E30

Acknowledgement

The research has been supported by National Natural Science Foundation of China (No. 11761047). The author thanks the referee for carefully reading the manuscript and for numerous thoughtful comments.