A Note on Cartan-Eilenberg Gorenstein categories

抄録

In this article, we investigate the stability of Cartan-Eilenberg Gorenstein categories. To this end, we introduce and study the concept of two-degree Cartan-Eilenberg $\mathcal{W}$-Gorenstein complexes. We prove that a complex C is two-degree Cartan-Eilenberg $\mathcal{W}$-Gorenstein if and only if C is Cartan-Eilenberg $\mathcal{W}$-Gorenstein. As applications, we show that a complex C is two-degree C-E Gorenstein projective if and only if C is C-E Gorenstein projective. Moreover, we obtain similar results for some known modules such as Ω-Gorenstein projective modules and V-Gorenstein projective modules.