… of complexes introduced by … complexes of relative Gorenstein flat modules, and provide a
characterisation for them as Gorenstein flat complexes relative to a certain class of complexes …

… We prove a similar characterization for chain complexes of R-modules: a complex X is Ding
projective (respectively, Ding injective, respectively, Ding flat) if and only if each component …

… Hat complexes are exact with Zn(F) flat for each n. Unfortunately the usual … a chain complex
A' for which X ® - is exact yet A' is not flat. Indeed X ® —is exact even if we just have A'„ flat …

… We call a chain complex of O-modules, F, flat if it is exact and each cycle ZnF is a flat O-module.
This definition agrees with the definition given in Definition 2.2 using the flat cotorsion …

… It follows from Neeman's characterization that a complex of flat modules F is pure acyclic
if and only if any chain map from a complex of projective modules to F is null-homotopic. In …

… module is defined to be ZnX/BnX and is denoted HnX. Given an R-module M, we let Sn(M)
denote the chain complex … We let Dn(M) denote the chain complex X with Xn = Xn−1 = M and …

… Now, since a module F is flat if and only if every short exact … of flat module is that of absolutely
pure (=FP-injective) module … , consequences for chain complexes of modules as we will …

… on the category of chain complexes over left R-modules, Ch(R−… exact) chain complexes.
Using a generalization of a well … -modules, and the category Ch(R−Mod) of chain complexes …

… ) complex of R-flat modules and F(p) is exact for every p ∈ SpecR, then F is K-flat (to be …
also prove that an (unbounded) complex P of R-projective modules is null-homotopic if P(p) …

… there, we prove that a chain complex F in a locally finitely … if and only if any chain map f : P
→ F from a complex P of pure-… , the chain complex M = h F of flat right C A -modules is pure …