One-Dimensional Local Rings with Finite Cohen-Macaulay Type

Abstract

Let (R,m) be a local ring of dimension one. Recall that a non-zero finitely generated R-module M is said to be a maximal Cohen-Macaulay module (MCM module for short) provided m contains a non-zero-divisor on M. Equivalently, the simple module R/ m does not embed in M. We say R has finite Cohen-Macaulay type (finite CM type) provided R has, up to isomorphism, only finitely many indecomposable MCM modules.