On the top local cohomology modules

On the annihilators and attached primes of top local cohomology modules

“…An important problem concerning local cohomology is determining the annihilators of the i th local cohomology module H i a (M). This problem has been studied by several authors; see for example [9], [10], [11], [14], [15], [16], and has led to some interesting results. More recently, in [2] Bahmanpour et al, proved an interesting result about the annihilator Ann R (H d m (M)), in the case (R, m) is a complete local ring of dimension d.…”

Annihilators of Top Local Cohomology Modules Defined by a Pair of Ideals

“…One of the basic problems concerning local cohomology modules is to determine the annihilators of them. This problem for ordinary local cohomology modules has been studied by several authors, see [6,7,8,9,11], and has led to some interesting results. In particular, Bahmanpour et al in [2] proved an interesting result about the annihilator of H d m (M ) the d-th local cohomology module of M , when (R, m) is a complete local ring and M is a non-zero finitely generated R-module with d = dim M .…”

Some results on the annihilators and attached primes of local cohomology modules

“…Among these properties, an interesting question is determining the annihilators of local cohomology modules. This problem has been studied by several authors; see for example [2], [3], [11], [12], [13], [16], [17], [19], and has led to some interesting results. A very interesting result shows that if R is regular local ring containing a field, then H i a (R) = 0, if and only if Ann R (H i a (R)) = 0, for all i ≥ 0, cf.…”