Local Cohomology with Respect to a Cohomologically Complete Intersection Pair of Ideals

Serre Subcategories and Local Cohomology Modules with Respect to a Pair of Ideals

This paper is concerned with the relation between local cohomology modules defined by a pair of ideals and the Serre subcategories of the category of modules. We characterize the membership of local cohomology modules in a certain Serre subcategory from lower range or upper range.

On formal local cohomology modules with respect to a pair of ideals

We introduce a generalization of formal local cohomology module, which we call a formal local cohomology module with respect to a pair of ideals and study its various properties. We analyze their structure, the upper and lower vanishing and non-vanishing. There are various exact sequences concerning the formal cohomology modules. Among them a MayerVietoris sequence for two ideals with respect t...

ON GRADED LOCAL COHOMOLOGY MODULES DEFINED BY A PAIR OF IDEALS

Let $R = bigoplus_{n in mathbb{N}_{0}} R_{n}$ be a standardgraded ring, $M$ be a finitely generated graded $R$-module and $J$be a homogenous ideal of $R$. In this paper we study the gradedstructure of the $i$-th local cohomology module of $M$ defined by apair of ideals $(R_{+},J)$, i.e. $H^{i}_{R_{+},J}(M)$. Moreprecisely, we discuss finiteness property and vanishing of thegraded components $H^...

Tameness of Local Cohomology of Monomial Ideals with Respect to Monomial Prime Ideals

In this paper we consider the local cohomology of monomial ideals with respect to monomial prime ideals and show that all these local cohomology modules are tame. Introduction Let R be a graded ring. Recall that a graded R-module N is tame, if there exists an integer j0 such that Nj = 0 for all j ≤ j0, or else Nj 6= 0 for all j ≤ j0. Brodmann and Hellus [4] raised the question whether for a fin...

a comparison of teachers and supervisors, with respect to teacher efficacy and reflection

supervisors play an undeniable role in training teachers, before starting their professional experience by preparing them, at the initial years of their teaching by checking their work within the proper framework, and later on during their teaching by assessing their progress. but surprisingly, exploring their attributes, professional demands, and qualifications has remained a neglected theme i...

Cofiniteness of Local Cohomlogy Based on a Non–Closed Support Defined by a Pair of Ideals