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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Short chains and regular components
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by Idun Reiten, Andrzej Skowroński and Sverre O. Smalø PDF
Proc. Amer. Math. Soc. 117 (1993), 601-612 Request permission

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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Additional Information
  • © Copyright 1993 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 117 (1993), 601-612
  • MSC: Primary 16G70; Secondary 16G10, 16G60
  • DOI: https://doi.org/10.1090/S0002-9939-1993-1124149-X
  • MathSciNet review: 1124149