An analogue of a theorem due to Levin and Vasconcelos

Details An analogue of a theorem due to Levin and Vasconcelos An analogue of a theorem due to Levin and Vasconcelos

2004-07-15

arxiv.org/abs/math/0407271v1

Mathematics

Commutative Algebra

7 pages. To appear in Contemporary Math

Scientific paper

Let $(R,\m)$ be a Noetherian local ring. Consider the notion of homological
dimension of a module, denoted H-dim, for H= Reg, CI, CI$_*$, G, G$^*$ or CM.
We prove that, if for a finite $R$-module $M$ of positive depth,
$\Hd_R({\m}^iM)$ is finite for some $i \geq \reg(M)$, then the ring $R$ has
property H.

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