A note on Gorenstein projective complexes

Authors

BO LU
LIU ZHONGKUI

DOI

10.3906/mat-1504-25

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.

Keywords

Gorenstein projective module, Cartan--Eilenberg projective complex, Gorenstein projective complex, $\mathcal{A}$ complex

First Page

235

Last Page

243

Recommended Citation

LU, BO and ZHONGKUI, LIU (2016) "A note on Gorenstein projective complexes," Turkish Journal of Mathematics: Vol. 40: No. 2, Article 1. https://doi.org/10.3906/mat-1504-25
Available at: https://journals.tubitak.gov.tr/math/vol40/iss2/1