On the local cohomology modules deffined by a pair of ideals and serre subcategories

TL;DR

This paper explores the relationship between local cohomology modules defined by pairs of ideals and Serre subcategories, extending previous results in the context of commutative Noetherian rings.

Contribution

It generalizes earlier findings by establishing new connections between local cohomology modules and Serre classes for modules over rings with pairs of ideals.

Findings

Established conditions for local cohomology modules to belong to Serre subcategories.

Extended previous results to broader classes of modules and ideals.

Provided new criteria for the structure of local cohomology modules.

Abstract

This paper is concerned about the relation between local cohomology modules defined by a pair of ideals and Serre classes of R-modules, as a generalization of results of J. Azami, R. Naghipour and B. Vakili (2009) and M. Asgharzadeh and M.Tousi (2010). Let R be a commutative Noetherian ring, I, J be two ideals of R and M be an R-module. Let a\in \~{W}(I; J) and t \in N_0 be such that Ext^t_R(R/a,M)\in S and Ext^j_R(R/a,H^i_I;J(M))\inS for all i < t and all j>=0. Then for any submodule N of H^t_I;J(M) such that Ext^1_R(R/a;N)\in,we obtain HomR(R=a;H^t_I;J(M)/N)\inS.