CHARACTERIZATION OF WEAKLY COFINITE LOCAL COHOMOLOGY MODULES

Let R be a commutative Noetherian ring, a an ideal of R, M an arbitrary R-module and X a finite R-module. We prove a characteri-zation for Hia(M) and Hia(X, M) to be a-weakly cofinite for all i, whenever one of the following cases holds: (a) ara(a) < 1, (b) dim R/a < 1 or (c) dim R < 2. We also prove that, if M is a weakly Laskerian R-module, then Hia(X, M) is a-weakly cofinite for all i, whenever dim X < 2 or dim M < 2 (resp. (R, m) a local ring and dim X < 3 or dim M < 3). Let d = dim M < oo, we prove an equivalent condition for top local cohomology module Hda(M) to be weakly Artinian.