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

Research output: Contribution to journal › Article › peer-review

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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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AB - 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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U2 - 10.1090/tran/7093

DO - 10.1090/tran/7093

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JF - Transactions of the American Mathematical Society

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Krull-Gabriel dimension of domestic string algebras

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