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2006.292: The Ziegler and Zariski spectra of some domestic string algebras

2006.292: Kevin Burke and Mike Prest (2002) The Ziegler and Zariski spectra of some domestic string algebras. Algebras and Representation Theory, 5 (3). pp. 211-234. ISSN 1572-9079

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DOI: 10.1023/A:1016581927685


It was a conjecture of the second author that the Cantor–Bendixson rank of the Ziegler spectrum of a finite-dimensional algebra is either less than or equal to 2 or is undefined. Here we refute this conjecture by describing the Ziegler spectra of some domestic string algebras where arbitrary finite values greater than 2 are obtained. We give a complete description of the Ziegler and Gabriel–Zariski spectra of the simplest of these algebras. The conjecture has been independently refuted by Schröer who, extending his work (1997) on these algebras, computed their Krull–Gabriel dimension.

Item Type:Article
Uncontrolled Keywords:string algebra - domestic representation type - Ziegler spectrum - pure-injective module - Cantor–Bandixon rank - Krull–Gabriel dimension - functor categories
Subjects:MSC 2000 > 03 Mathematical logic and foundations
MSC 2000 > 16 Associative rings and algebras
MIMS number:2006.292
Deposited By:Miss Louise Stait
Deposited On:15 August 2006

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