$\mathcal{VW}$-Gorenstein complexes

Authors : Renyu ZHAO, Wei REN

Pages : 537-547

View : 12 | Download : 8

Publication Date : 0000-00-00

Article Type : Research Paper

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 insert ignore into journalissuearticles values(resp., Gorenstein injective); complexes, and $G_C$-projective insert ignore into journalissuearticles values(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