A Krull-Schmidt theorem for one-dimensional rings of finite Cohen-Macaulay type |
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Authors: | Nicholas R. Baeth |
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Affiliation: | Department of Mathematics and Computer Science, Central Missouri State University, Warrensburg, MO 64093-5045, United States |
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Abstract: | This paper determines when the Krull-Schmidt property holds for all finitely generated modules and for maximal Cohen-Macaulay modules over one-dimensional local rings with finite Cohen-Macaulay type. We classify all maximal Cohen-Macaulay modules over these rings, beginning with the complete rings where the Krull-Schmidt property is known to hold. We are then able to determine when the Krull-Schmidt property holds over the non-complete local rings and when we have the weaker property that any two representations of a maximal Cohen-Macaulay module as a direct sum of indecomposables have the same number of indecomposable summands. |
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Keywords: | 13C14 13H10 16D70 16G50 |
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