Let R be a commutative Noetherian ring with identity, I be an ideal of R and M, N be two R-
modules. Throughout this paper, we denote by idR M and fdR M the injective dimension and …

Let R be a commutative Noetherian ring and I, J be ideals of R. Let M, N be two R-modules.
For an integer i≥ 0, we define the i-th generalized local cohomology module H< sub> I, J< …

Let be an ideal of a commutative Noetherian ring R, and let M and N be finitely generated R-
modules. Let be the-finiteness dimension of N. In this paper, among other things, we show …

The study of the cohomological dimension of algebraic varieties has produced some
interesting results and problems in local algebra. Let 𝔞 be an ideal of a commutative …

Let 𝔞 and 𝔟 be ideals of a commutative Noetherian ring R and M be a finitely generated R-
module of dimension d> 0. We prove some results concerning the top local cohomology and …

As a generalization of the ordinary local cohomology modules, recently some authors
introduced the local cohomology modules with respect to a pair of ideals. In this paper, we …

This paper is concerned to relationship between the sets of associated primes of the $ d $-
local cohomology modules and the ordinary local cohomology modules. Let $ R $ be a …

The first part of this paper is concerned with the Artinianness of certain local cohomology
modules when M is a Matlis reflexive module over a commutative Noetherian complete local …

Let Φ be a system of ideals of a noetherian ring R and M a finitely generated R-module. We
introduce the notion n-depth (Φ, M) and show that inf {i| dim Supp RH Φ i (M)> n}= n-depth …

Let R be a commutative Noetherian ring, let I be an ideal of R, and let M, N be two finitely
generated R-modules. The aim of this paper is to investigate the I-cofiniteness of …