… 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 …

… 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 …

… If f, g: X - Y are chain maps we say they are chain homotopic if there exists a collection of …
special chain complexes. Given an R-module M, we let S" (M) denote the chain complex with all …

… 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 …

… 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 …

… +(R-proj); that is, we will choose representatives of chain complexes up to isomorphism, not
up to homotopy equivalence. This means that there is a great deal of redundancy in the set T…

… In the case of finitely generated and projective extension of rings, the left version of condition
(i) in Lemma 2.5 implies that RA is in fact faithfully flat module (see, for example [5, Chap. I, …

… 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 …