The magnitude of a module category equals the Euler characteristic of its Auslander–Reiten quiver; for biserial algebras it equals the rank, and for hereditary type A_n it equals n.
On minimal representation-infinite algebras
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abstract
Over an algebraically closed field we classify all minimal representation-infinite algebras where the lattice of two-sided ideals is not distributive. As a consequence there are only finitely many isomorphism classes of minimal representation-infinite algebras in each dimension.
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Magnitude of module categories
The magnitude of a module category equals the Euler characteristic of its Auslander–Reiten quiver; for biserial algebras it equals the rank, and for hereditary type A_n it equals n.