On the Associated Primes of Generalized Local Cohomology Modules

Abstract

Let 𝔞 be an ideal of a commutative Noetherian ring R with identity and let M and N be two finitely generated R-modules. Let t be a positive integer. It is shown that is contained in the union of the sets , where 0 ≤ i ≤ t. As an immediate consequence, it follows that if either is finitely generated for all i < t or is finite for all i < t, then is finite. Also, we prove that if d = pd(M) and n = dim(N) are finite, then is Artinian. In particular, is a finite set consisting of maximal ideals.

Keywords:

• Associated prime ideals
• Generalized local cohomology
• Spectral sequences
• Weakly laskerian modules

2000 Mathematics Subject Classification:

• 13D45
• 13E99

Notes

Communicated by I. Swanson.