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Relations for Grothendieck groups of Artin algebras


Author: Maurice Auslander
Journal: Proc. Amer. Math. Soc. 91 (1984), 336-340
MSC: Primary 16A46; Secondary 16A54, 16A64, 18F30
DOI: https://doi.org/10.1090/S0002-9939-1984-0744624-1
MathSciNet review: 744624
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Abstract: M. C. R. Butler has shown that if $ \Lambda $ is an artin algebra of finite representation type, then the almost split sequences generate the relations for the Grothendieck group of $ \Lambda $. This paper is primarily devoted to proving the converse of Butler's result, i.e. $ \Lambda $ is of finite representation type if the almost split sequences generate the relations for the Grothendieck group of $ \Lambda $.


References [Enhancements On Off] (What's this?)

  • [1] M. Auslander and I. Reiten, Modules determined by their composition factors, Illinois J. Math. (to appear). MR 784524 (86i:16032)
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  • [5] M. C. R. Butler, Grothendieck groups and almost split sequences, Lecture Notes in Math., vol. 822, Springer-Verlag, Berlin and New York, 1981. MR 646111 (83k:18007)

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DOI: https://doi.org/10.1090/S0002-9939-1984-0744624-1
Article copyright: © Copyright 1984 American Mathematical Society

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