Krull–Gabriel dimension of domestic string algebras
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- by Rosanna Laking, Mike Prest and Gena Puninski PDF
- Trans. Amer. Math. Soc. 370 (2018), 4813-4840 Request permission
Abstract:
We calculate the Krull–Gabriel dimension of the category of modules over any domestic string algebra, in particular showing that it is finite, thus confirming a conjecture of Schröer. We also compute the Cantor–Bendixson rank of each point of its Ziegler spectrum and determine the topology on this space.References
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Additional Information
- Rosanna Laking
- Affiliation: School of Mathematics, Alan Turing Building, University of Manchester, Manchester M13 9PL, United Kingdom
- Address at time of publication: Max Planck Institute for Mathematics, Vivatsgasse 7, 53111 Bonn, Germany
- Email: rlaking@mpim-bonn.mpg.de
- Mike Prest
- Affiliation: School of Mathematics, Alan Turing Building, University of Manchester, Manchester M13 9PL, United Kingdom
- MR Author ID: 141975
- Email: mprest@manchester.ac.uk
- Gena Puninski
- Affiliation: Department of Mechanics and Mathematics, Belarusian State University, Praspekt Nezalezhnosti 4, Minsk 220030, Belarus
- Received by editor(s): May 19, 2016
- Received by editor(s) in revised form: September 27, 2016
- Published electronically: December 26, 2017
- Additional Notes: This paper was started during a visit of the third author to the University of Manchester, supported by EPSRC grant EP/K022490/1, and was completed during a visit of the second author to the Belarusian State University. The authors thank both universities and EPSRC for their support
- © Copyright 2017 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 370 (2018), 4813-4840
- MSC (2010): Primary 16G20, 16G60, 03C60
- DOI: https://doi.org/10.1090/tran/7093
- MathSciNet review: 3812097
Dedicated: Gena Puninski died on April 29, 2017. The other two authors dedicate this paper to his memory