Document Type
Article
Date
4-22-2003
Disciplines
Mathematics
Description/Abstract
Let (R,m,k) be a local Cohen-Macaulay (CM) ring of dimension one. It is known that R has finite CM type if and only if R is reduced and has bounded CM type. Here we study the one-dimensional rings of bounded but infinite CM type. We will classify these rings up to analytic isomorphism (under the additional hypothesis that the ring contains an infinite field). In the first section we deal with the complete case, and in the second we show that bounded CM type ascends to and descends from the completion. In the third section we study ascent and descent in higher dimensions and prove a Brauer-Thrall theorem for excellent rings.
Recommended Citation
Leuschke, Graham J. and Wiegand, Roger, "Local Rings of Bounded Cohen-Macaulay Type" (2003). Mathematics - All Scholarship. 29.
https://surface.syr.edu/mat/29
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, for more information see http://arxiv.org/abs/math/0211411