We study the existence of some covers and envelopes in the chain complex category of R-
modules. Let (𝒜, ℬ) be a cotorsion pair in R-Mod and let ℰ𝒜 stand for the class of all exact …

In this paper, we study completeness of cotorsion pairs in the category of complexes of R-
modules. Let (A, B) be a cotorsion pair in R-Mod. It is shown that the cotorsion pair …

Let R be a commutative noetherian ring. We give criteria for a complex of cotorsion flat R-
modules to be minimal, in the sense that every self homotopy equivalence is an …

A complex (C, δ) is called strongly Gorenstein flat if C is exact and Ker δ n is Gorenstein flat
in R-Mod for all n∈ ℤ. Let 𝒮𝒢 stand for the class of strongly Gorenstein flat complexes. We …

Let R be a right coherent ring and D b (R-Mod) the bounded derived category of left R-
modules. Denote by D^ b\left (R-Mod\right) _\left GF, C\right D b (R− M od) GF, C^ the …

We prove that, if GProj is the class of all Gorenstein projective modules over a ring R, then
GP=(GProj, GProj⊥) is a cotorsion pair. Moreover, GP is complete when all projective …

Let R be a ring and X a complex of R-modules. We give some characterizations of the
dimension of X related to special Gorenstein projective precovers. Let R be a ring such that …

We describe a general correspondence between injective (resp. projective) recollements of
triangulated categories and injective (resp. projective) cotorsion pairs. This provides a model …

We study homological behavior of modules satisfying the Auslander condition. Assume that
AC is the class of left R-modules satisfying the Auslander condition. It is proved that each …

In this paper we show that if the class f of R-modules is closed under well ordered direct
limits, then the class f is preenveloping in the category of R-modules if and only if the class …