… We also improve existing results on Tor-rigidity. This progress is driven by the existence
of minimal semi-flat-cotorsion replacements in the derived category as recently proved by …

… Finally, in Chapter 4, we study flat, cotorsion module theory with applications to rings of
characteristic p > 0. The theory of flat, cotorsion modules is in many ways “dual” to the theory of …

… using the theory of flat covers and minimal flat resolutions. … a large class of modules (ie,
cotorsion modules), which we show is … As Tor i R ( L , M ) = 0 for all i > 0 we have that L ⊗ R F is …

… We also improve existing results on Tor-rigidity. This progress is driven by the existence
of minimal semi-flat-cotorsion replacements in the derived category as recently proved by …

… vanishing of Ext; and highlights its relation with the rigidity of … n-rigid subcategory of Λ-Mod
if and only if {X ∈ Λ-Mod | Exti … -Leffler modules by using tools in model theory. He showed …

… , we survey the theory of Gorenstein homological dimensions … absolute Ext commutes with
localization, but the relative Ext is … to be cotorsion if Ext1 R(F,M) = 0 for every flat R-module F. …

… theory based on complete flat resolutions, which can form a correspondence with the classical
Tor … Let A, BfiºF, Cfi be the flat cotorsion pair in R-Mod. Then A (resp. B) complex and dg…

… explaining to me a lot of details in number theory and algebraic geometry. I also owe a lot to
… I learned a lot from him when we were going through problems in algebraic geometry and …

… cotorsion pairs in \(\mathcal{G}\), [34]. We refer to the survey [31] for more on this link between
approximation theory … T is a τ-rigid module provided there exists a projective presentation …