Turkish Journal of Mathematics
Abstract
As we know, a complex $Q$ is projective if and only if $Q$ is exact and $\mathrm{Z}_n(Q)$ is projective in $R$-$\mathrm{Mod}$ for each $n\in\mathbb{Z}$. 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 $\mathrm{Z}_n(G)$ is Gorenstein projective in $R$-$\mathrm{Mod}$ for each $n\in\mathbb{Z}$. Using the above result, a new equivalent characterization of some $\mathcal{A}$ complexes is obtained.
DOI
10.3906/mat-1504-25
Keywords
Gorenstein projective module, Cartan--Eilenberg projective complex, Gorenstein projective complex, $\mathcal{A}$ complex
First Page
235
Last Page
243
Recommended Citation
LU, B, & ZHONGKUI, L (2016). A note on Gorenstein projective complexes. Turkish Journal of Mathematics 40 (2): 235-243. https://doi.org/10.3906/mat-1504-25
