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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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 $\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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Additional Information

Lawrence S. Levy
Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706-1388
Email: levy@math.wisc.edu

Charles J. Odenthal
Affiliation: Department of Mathematics, University of Toledo, Toledo, Ohio 43606-3390
Email: codentha@math.utoledo.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-96-01619-4
PII: S 0002-9947(96)01619-4
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