Local Cohomology Modules, Serre Subcategories and Derived Functors of Torsion Functors

Abstract

In this research, by using filter regular sequences, we obtain some exact sequences of right or left derived functors of local cohomology modules. Then we use them to gain some conditions under which a right or left derived functor of some special functors over local cohomology modules belongs to a Serre subcategory. These results can conclude some generalizations of previous results in this context or regain some of them.

On the Behavior of Applying Derived Functors of Torsion Functors on Local Cohomology Modules

“…Note that D R (−) is a natural generalization of Matlis duality functor to non-local ring (see [23]). Since D R (−) is an exact functor, by using similar arguments to those used in [14,Lemma 2.2], one can obtain some exact sequences for D R (R j F (−)), D R (L j T (−)), R j F (D R (−)) and L j T (D R (−)), and so we can gain analogous of the results of this paper. As we did in this note, among some new results in this context, one can obtain some generalizations of previous ones such as [16,Theorem 3.4].…”

“…In this section we bring some exact sequences of derived functors of local cohomology modules from [14], which are needed in the sequel. Firstly, recall that an R-module M is called weakly Laskerian if the set of associated primes of any quotient module of M is finite (see [7]).…”

“…In this section, we exploit the obtained exact sequences in [14] to study the support and the set of associated prime ideals concerning to derived functors of torsion functors of certain modules. First, we begin by the following theorem.…”

“…There are a lot of papers devoted to studying the properties of (generalized) local cohomology modules or derived functors of these modules (e.g. [1,5,10,14,15,22]). …”

“…In this paper, by using some exact sequences gained in [14], we study the behavior of derived functors of special functors in a couple of directions. More precisely, in Sec.…”