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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 regular components


Authors: Idun Reiten, Andrzej Skowroński and Sverre O. Smalø
Journal: Proc. Amer. Math. Soc. 117 (1993), 601-612
MSC: Primary 16G70; Secondary 16G10, 16G60
MathSciNet review: 1124149
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Abstract: Let $ \Lambda $ be a finite-dimensional $ k$-algebra with $ k$ an algebraically closed field and $ \operatorname{ind} \Lambda $ a chosen subcategory of a complete set of isomorphism classes of finitely generated indecomposable $ \Lambda $-modules. This paper deals with the regular components of $ \operatorname{ind} \Lambda $ consisting of modules that are not the middle of any short chain. It is proved that the number of such components containing only a finite number of $ DTr$-orbits is finite. Further, the infinite radical of such a component is zero and the component is isomorphic to the mesh category of its underlying translation quiver. Families of selfinjective algebras having such components are constructed.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1124149-X
PII: S 0002-9939(1993)1124149-X
Article copyright: © Copyright 1993 American Mathematical Society