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 Schroer. We also compute the Cantor-Bendixson rank of each point of its Ziegler spectrum and determine the topology on this space.
Krull-gabriel dimension of domestic string algebras
Laking, R.
;Prest, M.;
2018
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 Schroer. 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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