On the formal grade of finitely generated modules over local rings
Abstract
Let \fa be an ideal of a local ring (R,\fm) and M a finitely generated R-module. This paper concerns the notion \fgrade(\fa,M), the formal grade of M with respect to \fa (i.e. the least integer i such that {\vpl}_nH^i_{\fm}(M/\fa^n M)\neq 0). We show that \fgrade(\fa,M)\geq \depth M-\cd_{\fa}(M), and as a result, we establish a new characterization of Cohen-Macaulay modules. As an application of this characterization, we show that if M is Cohen-Macaulay and L a pure submodule of M with the same support as M, then \fgrade(\fa,L)=\fgrade(\fa,M). Also, we give a generalization of the Hochster-Eagon result on Cohen-Macaulayness of invariant rings.
Keywords
Cite
@article{arxiv.0808.0653,
title = {On the formal grade of finitely generated modules over local rings},
author = {Mohsen Asgharzadeh and Kamran Divaani-Aazar},
journal= {arXiv preprint arXiv:0808.0653},
year = {2010}
}
Comments
This paper has been withdrawn by the authors, because it has been included as a section in arXiv:0807.5042