ABSTRACT
In this note, it is proven that if R is a right noetherian ring with and
for any left R-module F with finite flat dimension, then M is Gorenstein projective; if R is a left noetherian ring with idRR<∞ and M is a Gorenstein projective left R-module, then
for any left R-module F with finite flat dimension.
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.