Local Homology, Cohen-Macaulayness and Cohen-Macaulayfications

Details Local Homology, Cohen-Macaulayness and Cohen-Macaulayfications Local Homology, Cohen-Macaulayness and Cohen-Macaulayfications

2005-07-07

arxiv.org/abs/math/0507137v1

Mathematics

Commutative Algebra

5 pages

Scientific paper

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).

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