$\mathcal{VW}$-Gorenstein complexes

Authors : Renyu Zhao, Wei Ren

Pages : 537-547

View : 13 | Download : 7

Publication Date : 9999-12-31

Article Type : Makaleler

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.
Keywords : $mathcal{VW}$-Gorenstein complex, $mathcal{VW}$-Gorenstein module, stability