Krull-Schmidt theorems in dimension 1

Levy, Lawrence; Odenthal, Charles

doi:10.1090/S0002-9947-96-01619-4

Krull-Schmidt theorems in dimension 1
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by Lawrence S. Levy and Charles J. Odenthal

Trans. Amer. Math. Soc. 348 (1996), 3391-3455

DOI: https://doi.org/10.1090/S0002-9947-96-01619-4

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Abstract:

Let $\Lambda$ be a semiprime, module-finite algebra over a commutative noetherian ring $R$ of Krull dimension 1. We find necessary and sufficient conditions for the Krull-Schmidt theorem to hold for all finitely generated $\Lambda$-modules, and necessary and sufficient conditions for the Krull-Schmidt theorem to hold for all finitely generated torsionfree $\Lambda$-modules (called “$\Lambda$-lattices” in integral representation theory, and “maximal Cohen-Macaulay modules” in the dimension-one situation in commutative algebra).

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