Krull-Schmidt theorems in dimension 1
Authors: Lawrence S. Levy and Charles J. Odenthal
Journal: Trans. Amer. Math. Soc. 348 (1996), 3391-3455
MSC (1991): Primary 16P40; Secondary 13E05
MathSciNet review: 1351492
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Abstract: Let be a semiprime, module-finite algebra over a commutative noetherian ring of Krull dimension 1. We find necessary and sufficient conditions for the Krull-Schmidt theorem to hold for all finitely generated -modules, and necessary and sufficient conditions for the Krull-Schmidt theorem to hold for all finitely generated torsionfree -modules (called ``-lattices'' in integral representation theory, and ``maximal Cohen-Macaulay modules'' in the dimension-one situation in commutative algebra).
Lawrence S. Levy
Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706-1388
Charles J. Odenthal
Affiliation: Department of Mathematics, University of Toledo, Toledo, Ohio 43606-3390
Keywords: Krull-Schmidt, unique decomposition
Received by editor(s): April 11, 1994
Received by editor(s) in revised form: September 25, 1995
Additional Notes: Levy’s research was partially supported by NSF and NSA grants.
Article copyright: © Copyright 1996 American Mathematical Society