## 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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## Abstract

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 |
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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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