AUSLANDER-REITEN COMPONENTS CONTAINING MODULES WITH BOUNDED BETTI NUMBERS

摘要

Let R be a connected selfinjective Artin algebra, and H an indecomposable nonprojective R-module with bounded Betti numbers lying in a regular component of the Auslander-Reiten quiver of R. We prove that the Auslander-Reiten sequence ending at M has at most two indecomposable summands in the middle term. Furthermore we show that the component of the Auslander-Reiten quiver containing M is either a stable tube or of type ZA(infinity). We use these results to Study modules with eventually constant Betti numbers, and modules with eventually periodic Betti numbers.