$p$-torsion elements in local cohomology modules

Local Cohomology Modules Supported on Monomial Ideals

“…R. Hartshorne [41] va donar un exemple en el qual els nombres de Bass d'un mòdul de cohomologia local poden ser infinits si R noés regular. La finitud dels primers associats de H r I (R) per a qualsevol anell Noetherià R i qualsevol ideal I era una qüestió oberta fins que A. Singh [84] (cas no local) i M. Katzman [51] (cas local) han donat exemples de mòduls de cohomologia local amb infinits primers associats.…”

“…R. Hartshorne [41] gave an example of a local cohomology module whose Bass numbers may be infinite if R is not regular. The finiteness of the associated primes set of H r I (R) for any Noetherian ring R and any ideal I was an open question until A. Singh [84] (non local case) and M. Katzman [51] (local case) have given examples of local cohomology modules having infinite associated primes.…”

On the Associated Primes of Generalized Local Cohomology Modules

“…Singh [15] provides a counter example for this conjecture. However, it is known that the conjecture is true in many situations.…”

Associated Primes of Local Cohomology Modules of Weakly Laskerian Modules

“…Singh [16] gives a counter-example to this question (also see [17] for some other counter-examples). On the other hand, Brodmann and Lashgari [2,Theorem 2.2] showed that if for a finitely generated R-module M and an integer t, the local cohomology module H i a (M) is finitely generated for all i < t, then Ass R (H t a (M)) is finite.…”