Hossein Faridian

activity

20172024

most citedGorenstein Homology and Finiteness Properties of Local (Co)homology

2 citations · 3 across the 7 of their papers we have counts for

collaborators

9 papers

math.AC2024

Bounds on Gorenstein Dimensions and Exceptional Complete Intersection Maps

Hossein Faridian

We prove that if $f : R \to S$ is a local homomorphism of noetherian local rings of finite flat dimension and $M$ is a non-zero finitely generated $S$ -module whose Gorenstein…

math.AC2023

Bounds on Injective Dimension and Exceptional Complete Intersection Maps

Hossein Faridian

We prove that if $f : R \to S$ is a local homomorphism of noetherian local rings, and $M$ is a non-zero finitely generated or artinian $S$ -module whose injective dimension ov…

math.AC2020

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 $R$ , we present a characteriza…

math.AC2020★ 2 cited

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…

math.AC2017

Stable Under Specialization Sets and Cofiniteness

Kamran Divaani-Aazar, Hossein Faridian, Massoud Tousi

Let $R$ be a commutative noetherian ring, and $Z$ a stable under specialization subset of $\Spec(R)$. We introduce a notion of $Z$ -cofiniteness and study its ma…

math.AC2017

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…

math.AC2017

Local homology, finiteness of Tor modules and cofiniteness

Kamran Divaani-Aazar, Hossein Faridian, Massoud Tousi

Let $a$ be an ideal of a commutative noetherian ring $R$ with unity and $M$ an $R$ -module supported at $\V(\fa)$. Let $n$ be the supermum of the integers $i$ for which $H^{\f…

math.AC2017★ 1 cited

Local Homology, Koszul Homology and Serre Classes

Kamran Divaani-Aazar, Hossein Faridian, Massoud Tousi

Given a Serre class $S$ of modules, we compare the containment of the Koszul homology, Ext modules, Tor modules, local homology, and local cohomology in $S$ up…

math.AC2017

A New Outlook on Cofiniteness

Kamran Divaani-Aazar, Hossein Faridian, Massoud Tousi

Let $a$ be an ideal of a commutative noetherian (not necessarily local) ring $R$ . In the case $\cd(\mathfrak{a},R)\leq 1$, we show that the subcategory of $a$ …