In this paper, we introduce Gorenstein coat comodules and weakly Gorenstein injective
(resp. coat) comodules over any coalgebra C. We prove that, for a left semiperfect coalgebra …

We show that an iteration of the procedure used to define the Gorenstein projective modules
over a ring R yields exactly the Gorenstein projective modules. Specifically, given an exact …

We show that if a class of modules is closed under pure quotients, then it is precovering if
and only if it is covering, and this happens if and only if it is closed under direct sums. This is …

K-flatness for unbounded complexes of modules over a ring R was introduced by
Spaltenstein [27], as an analogue of the classical notion of flatness for modules. In this …

We prove that if the ring R is left noetherian andif the class of Gorenstein injective modules,
GI, is closed under ltrations, then GI is precovering. We extend this result to the category of …

We study homological aspects of Gorenstein flat modules over a ring with respect to a
duality pair (L, A). These modules are defined as cycles of exact chain complexes with …

Let R be a general ring. Duality pairs of R-modules were introduced by Holm-Jørgensen.
Most examples satisfy further properties making them what we call semi-complete duality …

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 …

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In this paper, we give a relationship between projective generators (resp., injective
cogenerators) in the category of R-modules and the counterparts in the category of …