… of the acyclic complexes of projective modules that remain acyclic … (R) is the smallest
projectively resolving class of modules that … are complete and hereditary cotorsion pairs in the …

… In this article, we introduce and study Gorenstein ( X , Y ) -flat modules as a … and complexes.
… A cotorsion pair ( A , B ) is said to be perfect if every module has an A -cover and a B -…

… flat modules are the modules in Z(Ac(Ch(Proj), ⊤Inj)), PGFlat. … that the module classes induced
by complexes defined in the … by a class of modules X, that is, the smallest definable class …

… the Tor-pair induced by the flat modules, we get the following … The X -precover f is said to be
an X -cover if it is minimal in the sense … As we mentioned before, if ( F, C ) is a cotorsion pair …

… , where we study complexes of flat R-contramodules using ℵ1-… only if it belongs to the minimal
full subcategory of Com(E) … of flat cotorsion R-contramodules and G• is a complex of flat R-…

… modules and FP n -flat modules have been studied in detail, generalized to chain complexes
and applications have been given to cotorsion … -coherent rings, the cotorsion pairs are well …

… GF(R) ∩ C(R) modulo flat-cotorsion modules and it is compactly generated when R has finite
… class generated by a class of modules X, that is, the smallest definable class containing X. …

… homotopy category of totally acyclic complexes. Moreover, we prove this is an equivalence
if C is the category of projective or flat-cotorsion S-modules. Dually, using divisibility in place …

… cotorsion and S-strongly flat R-modules, and show that all R-modules have S-strongly flat
covers if and only if all flat … of all minimal prime ideals in R, one has that the classes of flat and S…