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

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5 papers · 1 filter

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 $a$ …