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 …

In [13], Verdier introduced the notion of a Cartan–Eilenberg (CE) injective complex. Of
course, there is an obvious dual notion, that of a CE projective complex. In his paper, Verdier …

We study the notion of Cartan-Eilenberg Gorenstein projective N-complexes. We show that
an N-complex G is Cartan-Eilenberg Gorenstein projective if and only if Gn, Z nt (G), B nt (G) …

In this paper, we generalize the notion of Gorenstein projective modules. Namely, we
introduce X-Gorenstein projective modules, where X is a class of modules that contains all …

Let $\mathcal {V} $, $\mathcal {W} $, $\mathcal {Y} $, $\mathcal {X} $ be four classes of left $
R $-modules. The notion of $(\mathcal {V, W, Y, X}) $-Gorenstein $ R $-complexes is …

Enochs and Jenda gave some characterizations of Gorenstein injective and projective
complexes over n-Gorenstein rings. The aim of this article is to generalize these results and …

This paper introduces and studies (X, Y)-Gorenstein projective and injective modules, which
are a generalization of Enochs' Gorenstein projective and injective modules, respectively …

In this paper, we introduce and study the notions of Gorenstein n-FP-injective and
Gorenstein n-flat complexes, which are special cases of Gorenstein FP-injective and …

Let X and Y be N-complexes with N≥ 2 an integer such that X has finite Gorenstein
projective dimension and Y has finite Gorenstein injective dimension. We define the n th …

We show that over a right coherent left perfect ring R, a complex C of left R-modules is
Gorenstein projective if and only if C m is Gorenstein projective in R-Mod for all m∈ ℤ …