4 papers
A Note on Projective Modules
Hossein Faridian
This expository note delves into the theory of projective modules parallel to the one developed for injective modules by Matlis. Given a perfect ring , we present a characteriza…
Gorenstein Homology and Finiteness Properties of Local (Co)homology
Hossein Faridian
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…
Greenlees-May Duality in a Nutshell
Hossein Faridian
This expository article delves into the Greenlees-May Duality Theorem which is widely thought of as a far-reaching generalization of the Grothendieck's Local Duality Theorem. This…
Local homology, finiteness of Tor modules and cofiniteness
Kamran Divaani-Aazar, Hossein Faridian, Massoud Tousi
Let be an ideal of a commutative noetherian ring with unity and an -module supported at $\V(\fa)$. Let be the supermum of the integers for which $H^{\f…