Turkish Journal of Mathematics
Abstract
Let $\mathcal{V,W}$ be two classes of modules. In this paper, we introduce and study $\mathcal{VW}$-Gorenstein complexes as a common generalization of $\mathcal{W}$-complexes, Gorenstein projective (resp., Gorenstein injective) complexes, and $G_C$-projective (resp., $G_C$-injective) complexes. It is shown that under certain hypotheses a complex $X$ is $\mathcal{VW}$-Gorenstein if and only if each $X^n$ is a $\mathcal{VW}$-Gorenstein module. This result unifies the corresponding results of the aforementioned complexes. As an application, the stability of $\mathcal{VW}$-Gorenstein complexes is explored.
DOI
10.3906/mat-1603-88
Keywords
$\mathcal{VW}$-Gorenstein complex, $\mathcal{VW}$-Gorenstein module, stability
First Page
537
Last Page
547
Recommended Citation
ZHAO, RENYU and REN, WEI
(2017)
"$\mathcal{VW}$-Gorenstein complexes,"
Turkish Journal of Mathematics: Vol. 41:
No.
3, Article 7.
https://doi.org/10.3906/mat-1603-88
Available at:
https://journals.tubitak.gov.tr/math/vol41/iss3/7
