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Cycles in Module Categories

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Finite Dimensional Algebras and Related Topics

Part of the book series: NATO ASI Series ((ASIC,volume 424))

Abstract

Let A be an artin algebra over a commutative artin ring R and mod A be the category of finitely generated right A-modules. A cycle in mod A is a sequence of non-zero non-isomorphisms M 0 → M 1 → ... → M n = M 0 between indecomposable modules from mod A. The main aim of this survey article is to show that study of cycles in mod A leads to interesting information on indecomposable A-modules, the Auslander-Reiten quiver of A, and the ring structure of A. We present recent advances in some areas of the representation theory of artin algebras which should be of interest to a wider audience. In the paper, we also pose a number of open problems and indicate some new research directions.

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Author information

Authors and Affiliations

  1. Institute of Mathematics, Nicholas Copernicus University, Chopina 12/18, 87-100, Toruń, Poland

    Andrzej Skowroński

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  1. Andrzej Skowroński
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Editors and Affiliations

  1. Department of Mathematics and Statistics, Carleton University, K1S 5B6, Ottawa, Ontario, Canada

    Vlastimil Dlab

  2. Department of Mathematics, University of Virginia, 22901, Charlottesville, Virginia, USA

    Leonard L. Scott

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© 1994 Springer Science+Business Media Dordrecht

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Skowroński, A. (1994). Cycles in Module Categories. In: Dlab, V., Scott, L.L. (eds) Finite Dimensional Algebras and Related Topics. NATO ASI Series, vol 424. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1556-0_17

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  • DOI: https://doi.org/10.1007/978-94-017-1556-0_17

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4377-1

  • Online ISBN: 978-94-017-1556-0

  • eBook Packages: Springer Book Archive

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