Abstract
The first part of this paper is concerned with the Artinianness of certain local cohomology modules [Formula: see text] when M is a Matlis reflexive module over a commutative Noetherian complete local ring R and 𝔞 is an ideal of R. Also, we characterize the set of attached prime ideals of [Formula: see text], where n is the dimension of M. The second part is concerned with the vanishing of local cohomology and generalized local cohomology modules. In fact, when R is an arbitrary commutative Noetherian ring, M is an R-module and 𝔞 is an ideal of R, we obtain some lower and upper bounds for the cohomological dimension of M with respect to 𝔞.
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