… exact when applying a functor Hom(−,F), with F any flat module. It … We use SFPI to denote
the class of strongly FP-injective … of strongly FP-injective modules is simply that of FP-injective …

… of injective modules, FP-injective modules, absolutely clean … with respect to relative Gorenstein
flat modules. All kinds of … and flat modules staying exact when applying some functors at …

… The notion of strongly Gorenstein projective, injective and flat … of strongly Gorenstein-projective,
injective and flat modules over … pure projective modules and FP-injective modules over …

… We also considered Cartan-Eilenberg FP-injective complexes in [9]. In this paper, our main
… functor HomR(−,F) leaves P exact whenever F is flat. In this case, we say that P is a strongly …

… As an application, it is proved that R is (strongly) CM-free if and only if R has finite weak … ,
flat and FP-injective) modules in R-Mod is denoted by R-Proj (respectively, R-Inj, R-Flat and R-…

… We also introduce the class of strongly G W -flat modules. … the right homological functor (in
our case the Tor functor), and … Then, the module W = ⊕ i ≥ 0 F i is FP-injective, so since R is …

… Ding, Li, and Mao [Citation12] studied special cases of Gorenstein projective and Gorenstein
injective modules, which they called strongly Gorenstein flat and FP-injective modules …

… and Gorenstein derived functors. Holm’s results point out the strong relation between the …
in the next section the corresponding property of “being strongly hereditary” for \({\mathcal {S}}\)-…

… it is strongly cotorsion, and a right \(R\)-module is Gorenstein flat if and only if it is strongly
torsion… Dually, an \(R\)-module \(N\) is said to be Ding injective (Gorenstein FP-injective) if there …

… , flat and FP-injective) … strongly CM-free if \(_R\mathcal{G}\mathcal{P}=~_R\mathcal {P}\).
As the second application of Theorem 3.5, we will characterize the strongly CM-freeness of flat-…