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Transactions of the American Mathematical Society

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Krull-Gabriel dimension of domestic string algebras


Authors: Rosanna Laking, Mike Prest and Gena Puninski
Journal: Trans. Amer. Math. Soc. 370 (2018), 4813-4840
MSC (2010): Primary 16G20, 16G60, 03C60
DOI: https://doi.org/10.1090/tran/7093
Published electronically: December 26, 2017
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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.


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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
Email: mprest@manchester.ac.uk

Gena Puninski
Affiliation: Department of Mechanics and Mathematics, Belarusian State University, Praspekt Nezalezhnosti 4, Minsk 220030, Belarus

DOI: https://doi.org/10.1090/tran/7093
Keywords: Domestic string algebra, Krull--Gabriel dimension, Cantor--Bendixson rank, m-dimension, Ziegler spectrum, pure-injective module, transfinite radical, pointed module, pp formula
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
Dedicated: Gena Puninski died on April 29, 2017. The other two authors dedicate this paper to his memory
Article copyright: © Copyright 2017 American Mathematical Society

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