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

 

Module categories without short cycles are of finite type


Authors: Dieter Happel and Shi Ping Liu
Journal: Proc. Amer. Math. Soc. 120 (1994), 371-375
MSC: Primary 16D90; Secondary 16G10, 16G60
MathSciNet review: 1164144
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Abstract: Let $ A$ be an artin algebra. An indecomposable finitely generated $ A$-module $ X$ is said to be on a short cycle if there exists an indecomposable finitely generated $ A$-module $ Y$ and two nonzero noninvertible maps $ f:X \to Y$ and $ g:Y \to X$. If there are no short cycles we show that there exist only finitely many indecomposable $ A$-modules up to isomorphism.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1164144-9
PII: S 0002-9939(1994)1164144-9
Article copyright: © Copyright 1994 American Mathematical Society