Krull-Gabriel dimension of domestic string algebras

Rosanna Laking; Michael Prest; Gennady Puninskiy

doi:10.1090/tran/7093

Krull-Gabriel dimension of domestic string algebras

Rosanna Laking, Michael Prest, Gennady Puninskiy

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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.

Original language	English
Pages (from-to)	4813-4840
Journal	Transactions of the American Mathematical Society
Volume	370
Issue number	0
Early online date	26 Dec 2017
DOIs	https://doi.org/10.1090/tran/7093
Publication status	Published - 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 Schr{\"o}er. 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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Krull-Gabriel dimension of domestic string algebras

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