This thesis is comprised of three chapters. The first chapter deals with bounded complexes
of Gorenstein projective and Gorenstein injective modules. Deploying methods of relative …

Given a Serre class S of modules, we compare the containment of Koszul homology, Ext
modules, Tor modules, local homology and local cohomology in S up to a given bound s≧0 …

Let $ R $ be a commutative Noetherian ring, $ fa $ anideal of $ R $ and $ mathcal {D}(R) $
denote the derived category of $ R $-modules. For any homologically bounded complex $ X …