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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Short chains and short cycles of modules

Authors: I. Reiten, A. Skowroński and S. O. Smalø
Journal: Proc. Amer. Math. Soc. 117 (1993), 343-354
MSC: Primary 16G10; Secondary 16G70
MathSciNet review: 1136238
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Abstract: We show that for a large class of artin algebras including the algebras of finite representation type, an indecomposable module $ M$ is not the middle of a short chain if and only if there is no short cycle $ M \to N \to M$ of nonzero nonisomorphisms between indecomposable modules. We apply this to get sufficient conditions for modules to be determined by their composition factors. We also show that if for an algebra of finite representation type there is a sincere indecomposable $ \Lambda $-module that is not the middle of a short chain, then $ \Lambda $ is a tilted algebra.

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PII: S 0002-9939(1993)1136238-4
Keywords: Short chains, short cycles, tilted algebras
Article copyright: © Copyright 1993 American Mathematical Society