… Now assembling the sequences (†) and (‡), we get a totally acyclic complex of flat R-… such
that Ti = 0 for each i < −1, T−1 is Gorenstein flat and cotorsion, and Ti is flat and cotorsion for …

… Homotopy category theory is an important field in the study for homological algebra (refer to
[… Moreover, G is a Gorenstein flat complex of R-modules if and only if Gi is a Gorenstein flat R-…

… of cotorsion pairs in modules categories (see [35]). Apart from its original habitat of module
… , A ∈ A the complex HomA(A , A) is H-projective in Hk. We say that A is k-flat if for each pair …

… ., hereditary) cotorsion pair. A pair (ℱ,𝒞) of classes of modules is called a cotorsion pair or
cotorsion theory provided … are called therein strongly Gorenstein flat. Since strongly Gorenstein …

… has found many applications in representation theory and … that a complex of left R-modules
F is K-flat if the complex of … We say that the cotorsion pair is complete if for any object A ∈ A …

… Also, in the last section, we prove some new results on flat … We start by recalling the fundaments
of the theory of cotorsion … would be the n-term silting complexes, which we do not discuss …

… noncommutative rings, the theory for commutative rings worked … complex of projective (or
even flat) R-modules, we call it M-… ( W , GI ) is an injective cotorsion pair and that its associated …

… cotorsion pairs, which is Ext-version of torsion theory. Approximations coming from cotorsion
… the class of Ntotally acyclic complexes, that is, exact complexes of flat R-modules which …

… We show that when R is noetherian the class of N-totally acyclic complexes of flat modules
is … Also, for each N-totally acyclic complex D, we have that D is in Gor Flat, so Ext1(D, K) = 0. …