A note on Gorenstein projective complexes

Abstract

As we know, a complex Q is projective if and only if Q is exact and Zn(Q) is projective in R-Mod for each n ∈ Z. In this article, we show that a complex G is Gorenstein projective with Hom R(P, G) and Hom R(G, P) exact for any Cartan-Eilenberg projective complex P if and only if G is exact and Zn(G) is Gorenstein projective in R-Mod for each n ∈ Z. Using the above result, a new equivalent characterization of some A complexes is obtained.