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 …

Let R be an arbitrary associated ring. For an integer N⩾ 2 and a self-orthogonal subcategory
WW of R-modules, we study the notion of Cartan-Eilenberg W WN-complexes. We show that …

For an integer N≥ 2 and three subcategories 𝒲, 𝒳, 𝒴 of modules, we study the notion of (𝒲,
𝒳, 𝒴)-Gorenstein N-complexes. We show that under certain hypotheses, an N-complex C is …

We show that an N-complex of modules C is FP-injective if and only if C is N-exact and Z ni
(C) is an FP-injective module for each i= 1, 2,⋯, N and each n∈ Z by virtue of Gaussian …

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) …

Cartan-Eilenberg Gorenstein-injective m-complexes Page 1 http://www.aimspress.com/journal/Math
AIMS Mathematics, 6(5): 4306–4318. DOI:10.3934/math.2021255 Received: 30 October …