Author: Grigory Garkusha

Paper: Relative homological algebra for the proper class omega_f

Abstract: The proper class of f-monomorphisms is introduced. The 
corresponding relatively injective (respectively FP-injective and flat) 
modules are pure-injective fp-injective (respectively fp-injective and 
fp-flat) modules. The relative (co)homological functors $\Ext_f$ and 
$\Tor^f$ as well as the corresponding dimensions for rings and modules 
are studied. Moreover, it is shown that the relative derived category 
$D^+_f(R)$ and the derived category of the locally coherent Grothendieck 
category (mod-R,Ab)/lim S^R as well as K-theory K'(R)=K(R-mod) for 
the category of finitely presented left modules and K-theory of the 
abelian category of coherent objects of (mod-R,Ab)/lim S^R are naturally equivalent.