Let (R,m) be a Noetherian local ring and I an ideal of R. Let M be a finitely generated R-module with dim M=d. It is clear by Matlis duality that if R is complete then H^d_I(M) satisfies the following property: Ann_R(0:_{H^d_I(M)}p=p for all prime ideals p containing Ann_RH^d_I(M). However, H^d_I(M) does not satisfy this property in general. In this paper we characterize this property  of H^d_I(M) in order to study the catenarity of the ring R/Ann_RH^d_I(M), the set of attached primes of H^d_I(M), the co-support  of H^d_I(M), and the multiplicity of H^d_I(M). We also show that if H^d_I(M) satisfies this property then H^d_I(M) is isomorphic to some top local cohomology module with respect to the maximal ideal.

Tải file On the top local cohomology modules, J. Algebra (SCI) 349 (2012), 342-352. tại đây