Abstract
Assume that K is an algebraically closed field, R a locally support-finite locally bounded K-category, G a torsion-free admissible group of K-linear automorphisms of R and A=R/G. We show that the Krull-Gabriel dimension KG(R) of R equals the Krull-Gabriel dimension KG(A) of A. Furthermore, we determine the Krull-Gabriel dimension of locally support-finite repetitive K-categories. These results are applied to determine the Krull-Gabriel dimension of standard selfinjective algebras of polynomial growth. Finally, we show that there are no super-decomposable pure-injective modules over standard selfinjective algebras of domestic type.
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