Local rings of bounded Cohen-Macaulay type

Graham J. Leuschke, Roger Wiegand

Research output: Contribution to journalArticle

8 Scopus citations

Abstract

Let(R, m, k) be a complete 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.

Original languageEnglish (US)
Pages (from-to)225-238
Number of pages14
JournalAlgebras and Representation Theory
Volume8
Issue number2
DOIs
StatePublished - May 2005

Keywords

  • Bounded Cohen-Macaulay type
  • Brauer-Thrall theorem
  • Maximal Cohen-Macaulay module

ASJC Scopus subject areas

  • Mathematics(all)

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