Indecomposable modules of large rank over Cohen-Macaulay local rings

Abstract

A commutative Noetherian local ring (R, m, k) is called Dedekind-like provided R is one-dimensional and reduced, the integral closure R is generated by at most 2 elements as an R-module, and m is the Jacobson radical of R. If M is an indecomposable finitely generated module over a Dedekind-like ring R, and if P is a minimal prime ideal of R, it follows from a classification theorem due to L. Klingler and L. Levy that M p must be free of rank 0, 1 or 2. Now suppose (R, m, k) is a one-dimensional Cohen-Macaulay local ring that is not Dedekind-like, and let P 1 ,... P t be the minimal prime ideals of R. The main theorem in the paper asserts that, for each non-zero t-tuple (n 1 ,... n t ) of non-negative integers, there is an infinite family of pairwise non-isomorphic indecomposable finitely generated R-modules M satisfying MP i ≅ (Rp i ) (n i ) for each i.