  Let (R,m) be a local, complete ring, X an artinian R-module of Noetherian
dimension d; let x_1,...,x_d\in m be such that 0:_X (x_1,...,x_d)R has finite
length. Then H^x_d(X) is a finite R-module, providing a positive answer to a
question posed by Tang. As a first application of this result corollory 1
contains a necessary condition for a finite module to be CM; secondly we
propose a notion of Cohen-Macaulayfication and prove its uniqueness (th. 3);
finally we show that this new notion of Cohen-Macaulayfication is a direct
generalization of a notion of Cohen-Macaulayfication introduced by Goto (th.
4).
