Abstract

It was a conjecture of the second author that the Cantor-Bendixson rank of the Ziegler spectrum of a nite-dimensional algebra is either less than or equal to 2 or is undened. Here we refute this conjecture by describing the Ziegler spectra of some domestic string algebras where arbitrary nite 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 Schroer [21] who, extending his work [20] on these algebras, computed their Krull-Gabriel dimension. 1 Indecomposable pure-injectives over domestic string algebras 12 Let R be a domestic string algebra over an arbitrary eld k. Modules will generally be left R-modules: the category of these we denote by R-Mod. 1 This work was done while the rst author was supported by EPSRC grant number GR/K19686. Both authors thank the EPSRC for this nancial support. 2 Primary: 16G20; Secondary: 03C60,...

Citations