Geodesic
A characterization of representation-finite algebras
Fundamenta Mathematicae, Tome 140 (1991) no. 1, pp. 31-34 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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Let A be a finite-dimensional, basic, connected algebra over an algebraically closed field. Denote by Γ(A) the Auslander-Reiten quiver of A. We show that A is representation-finite if and only if Γ(A) has at most finitely many vertices lying on oriented cycles and finitely many orbits with respect to the action of the Auslander-Reiten translation. 
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Andrzej Skowroński; M. Wenderlich. A characterization of representation-finite algebras. Fundamenta Mathematicae, Tome 140 (1991) no. 1, pp. 31-34. doi: 10.4064/fm-140-1-31-34

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