An analogue of a theorem due to Levin and Vasconcelos

Javad Asadollahi; Tony J. Puthenpurakal

An analogue of a theorem due to Levin and Vasconcelos

Commutative Algebra 2007-05-23 v1

Authors: Javad Asadollahi , Tony J. Puthenpurakal

Abstract

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.

Keywords

noetherian local ring homological dimension finite module positive depth property h

Cite

@article{arxiv.math/0407271,
  title  = {An analogue of a theorem due to Levin and Vasconcelos},
  author = {Javad Asadollahi and Tony J. Puthenpurakal},
  journal= {arXiv preprint arXiv:math/0407271},
  year   = {2007}
}

Comments

7 pages. To appear in Contemporary Math

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