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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Krull-Schmidt fails for serial modules


Author: Alberto Facchini
Journal: Trans. Amer. Math. Soc. 348 (1996), 4561-4575
MSC (1991): Primary 16D70, 16S50, 16P60
DOI: https://doi.org/10.1090/S0002-9947-96-01740-0
MathSciNet review: 1376546
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Abstract: We answer a question posed by Warfield in 1975: the Krull-Schmidt Theorem does not hold for serial modules, as we show via an example. Nevertheless we prove a weak form of the Krull-Schmidt Theorem for serial modules (Theorem 1.9). And we show that the Grothendieck group of the class of serial modules of finite Goldie dimension over a fixed ring $R$ is a free abelian group.


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Additional Information

Alberto Facchini
Affiliation: Dipartimento di Matematica e Informatica, Università di Udine, 33100 Udine, Italy
Email: facchini@dimi.uniud.it

DOI: https://doi.org/10.1090/S0002-9947-96-01740-0
Received by editor(s): August 4, 1995
Additional Notes: Partially supported by Ministero dell’Università e della Ricerca Scientifica e Tecnologica (Fondi 40% e 60%), Italy. This author is a member of GNSAGA of CNR
Article copyright: © Copyright 1996 American Mathematical Society