Associated Primes of Local Cohomology Modules of Weakly Laskerian Modules

ABSTRACT

The notion of weakly Laskerian modules was introduced recently by the authors. Let R be a commutative Noetherian ring with identity, 𝔞 an ideal of R, and M a weakly Laskerian module. It is shown that if 𝔞 is principal, then the set of associated primes of the local cohomology module is finite for all i ≥ 0. We also prove that when R is local, then is finite for all i ≥ 0 in the following cases: (1) dim R ≤ 3, (2) dim R/𝔞 ≤ 1, (3) M is Cohen-Macaulay, and for any ideal 𝔟, with l = grade(𝔟, M), is weakly Laskerian.

Key Words:

• Associated prime ideals
• Cofiniteness
• Local cohomology
• Spectral sequences
• Weakly Laskerian modules

2000 Mathematics Subject Classification:

• 13D45
• 13E99

Notes

Communicated by I. Swanson.