Some results on associated primes of local cohomology modules

抄録

The paper contributes to the question whether the set of associated prime ideals of the local cohomology module Hⁱ_I (M) is finite for all ideals I of a local ring (R, m) and a finitely generated generalized Cohen-Macaulay R-module M. We prove that it will be enough to solve the problem for i=2 resp. 3 for ideals with two resp. certain ideals with three generators. This extends Hellus' result, see [5], of a Cohen-Macaulay ring. Moreover, in the case of M a Cohen-Macaulay module there is another sufficient criterion for the finiteness of associated prime ideals of Hⁱ_I (M) related to certain cofiniteness conditions. Finally, we discuss several examples of the literature related to the problem.