Document Type
Article
Date
4-3-2006
Embargo Period
11-15-2011
Disciplines
Mathematics
Description/Abstract
We study the growth of the Betti sequence of the canonical module of a Cohen-Macaulay local ring. It is an open question whether this sequence grows exponentially whenever the ring is not Gorenstein. We answer the question of exponential growth affirmatively for a large class of rings, and prove that the growth is in general not extremal. As an application of growth, we give criteria for a Cohen-Macaulay ring possessing a canonical module to be Gorenstein.
Recommended Citation
Jorgensen, David A. and Leuschke, Graham J., "On the Growth of the Betti Sequence of the Canonical Module" (2006). Mathematics Faculty Scholarship. Paper 35.
http://surface.syr.edu/mat/35
Source
Harvested from arXiv.org
Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.
Additional Information
This manuscript is from arXiv.org, more information see http://arxiv.org/abs/math/0603693