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Indecomposable modules of large rank over Cohen-Macaulay local rings

Authors:	Wolfgang Hassler Ryan Karr Lee Klingler Roger Wiegand

Institution:	Institut für Mathematik und wissenschaftliches Rechnen, Karl-Franzens-Universität Graz, Heinrichstraße 36/IV, A-8010 Graz, Austria Ryan Karr ; Honors College, Florida Atlantic University, Jupiter, Florida 33458 Lee Klingler ; Department of Mathematical Sciences, Florida Atlantic University, Boca Raton, Florida 33431-6498 Roger Wiegand ; Department of Mathematics, University of Nebraska-Lincoln, Lincoln, Nebraska 68588-0130

Abstract:	A commutative Noetherian local ring $(R,\mathfrak{m},k)$ is called Dedekind-like provided is one-dimensional and reduced, the integral closure $\overline{R}$ is generated by at most 2 elements as an -module, and $\mathfrak{m}$ is the Jacobson radical of $\overline{R}$ . If is an indecomposable finitely generated module over a Dedekind-like ring , and if is a minimal prime ideal of , it follows from a classification theorem due to L. Klingler and L. Levy that must be free of rank 0, 1 or 2. Now suppose $(R,\mathfrak{m},k)$ is a one-dimensional Cohen-Macaulay local ring that is not Dedekind-like, and let $P_1,\dotsc,P_t$ be the minimal prime ideals of . The main theorem in the paper asserts that, for each non-zero -tuple $(n_1,\dotsc,n_t)$ of non-negative integers, there is an infinite family of pairwise non-isomorphic indecomposable finitely generated -modules satisfying $M_{P_i}\cong(R_{P_i})^{(n_i)}$ for each .

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